<?xml version="1.0"?>
<div class="add">

<a NAME="E1:46"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>;<br/>
<span class="lab"><font color="Green" title="E45">A2</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 2</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
<br/>.= 
4
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>
;<br/>
<span class="lab"><font color="Green" title="E46">A3</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
<br/>.= 
16
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>
;<br/>
<span class="lab"><font color="Green" title="E47">A4</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 8</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 4</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
<span class="p1">(<span class="default">16 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 16</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
<br/>.= 
256
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>
;<br/>
<a NAME="E5:46"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
4001 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 32
 
;<br/>
<a NAME="E6:46"/>
256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 16</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1520
 
;<br/>
<a NAME="E7:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<span class="p1">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1520
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<span class="lab"><font color="Green" title="E50">A7</font></span>: <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">5 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5

<br/>.= 
<span class="p1">(<span class="default">5 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 5
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T6" onmouseover="rs('newton/T6')" onmouseout="rh()">NEWTON:6</a></span>
<br/>.= 
5 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T6" onmouseover="rs('newton/T6')" onmouseout="rh()">NEWTON:6</a></span>
<br/>.= 
5 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 3

;<br/>
<a NAME="E9:46"/>
1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1023 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 261</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2268
 
;<br/>
<a NAME="E10:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<span class="p1">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1023</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2268
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E11:46"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prepower.html#T11" onmouseover="rs('prepower/T11')" onmouseout="rh()">PREPOWER:11</a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E12:46"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
6311 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2310
 
;<br/>
<a NAME="E13:46"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1913 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1867</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2311
 
;<br/>
<a NAME="E14:46"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 693</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1913
 
;<br/>
<a NAME="E15:46"/>
3441 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3441 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2959</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1522
 
;<br/>
<a NAME="E16:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A13</font></span>: 
<span class="p1">(<span class="default">3441 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3441</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1522
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E17:46"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2164 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 553</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1219
 
;<br/>
<a NAME="E18:46"/>
2499 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2499 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1560</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3441
 
;<br/>
<a NAME="E19:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A15</font></span>: 
<span class="p1">(<span class="default">2499 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2499</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3441
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E20:46"/><span class="lab"><font color="Green" title="E59">A16</font></span>: 
3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 988 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 964</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2164
 
;<br/>
<a NAME="E21:46"/>
1823 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 830</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2499
 
;<br/>
<a NAME="E22:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A17</font></span>: 
<span class="p1">(<span class="default">1823 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2499
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E23:46"/><span class="lab"><font color="Green" title="E61">A18</font></span>: 
1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3376 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1284</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 988
 
;<br/>
<a NAME="E24:46"/>
1520 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1520 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 577</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1823
 
;<br/>
<a NAME="E25:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A19</font></span>: 
<span class="p1">(<span class="default">1520 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1520</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1823
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E26:46"/><span class="lab"><font color="Green" title="E63">A20</font></span>: 
3441 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1567</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3376
 
;<br/>
<a NAME="E27:46"/>
1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1522 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 578</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3906
 
;<br/>
<a NAME="E28:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A21</font></span>: 
<span class="p1">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1522</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3906
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<a NAME="E29:46"/><span class="lab"><font color="Green" title="E65">A22</font></span>: 
2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1219 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 691</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
;<br/>
<a NAME="E30:46"/>
3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3906 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3813</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1023
 
;<br/>
<a NAME="E31:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A23</font></span>: 
<span class="p1">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3906</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1023
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>;<br/>
<span class="lab"><font color="Green" title="E67">A24</font></span>: 4001 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 = 
4001 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>
<br/>.= 
4000

;<br/>
<span class="lab"><font color="Green" title="E68">A25</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 16</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 8</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
1520
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:46"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E7:46"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E69">A26</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 32</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 16</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
1823
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:46"><span class="lab"><font color="Green" title="E68">A25</font></span></a>, <a class="txt" href="#E25:46"><span class="lab"><font color="Green" title="E62">A19</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E70">A27</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 64</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
2499
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:46"><span class="lab"><font color="Green" title="E69">A26</font></span></a>, <a class="txt" href="#E22:46"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E71">A28</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 128</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 64</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
3441
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:46"><span class="lab"><font color="Green" title="E70">A27</font></span></a>, <a class="txt" href="#E19:46"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E72">A29</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 256</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 128</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
1522
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:46"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="txt" href="#E16:46"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E73">A30</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 512</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
3906
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:46"><span class="lab"><font color="Green" title="E72">A29</font></span></a>, <a class="txt" href="#E28:46"><span class="lab"><font color="Green" title="E64">A21</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E74">A31</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1024</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 512</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
1023
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:46"><span class="lab"><font color="Green" title="E73">A30</font></span></a>, <a class="txt" href="#E31:46"><span class="lab"><font color="Green" title="E66">A23</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="lab"><font color="Green" title="E75">A32</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">512 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 288</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 512</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 288</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default">256 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:46"><span class="lab"><font color="Green" title="E73">A30</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:46"><span class="lab"><font color="Green" title="E69">A26</font></span></a>, <a class="txt" href="#E37:46"><span class="lab"><font color="Green" title="E72">A29</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1913</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:46"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
2311
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:46"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
;<br/>
<a NAME="E41:46"/>
4000 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 800</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E76">A33</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4001 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 5</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 4001 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:46"><span class="lab"><font color="Green" title="E67">A24</font></span></a>, <a class="ref" href="nat_d.html#D1" onmouseover="rs('nat_d/D1')" onmouseout="rh()">NAT_D:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default">4001 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
4001 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 800</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4000</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:46"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="ref" href="nat_d.html#T28" onmouseover="rs('nat_d/T28')" onmouseout="rh()">NAT_D:28</a></span>
<br/>.= 
4001 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2311 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default">4000 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:46"><span class="lab"><font color="Green" title="E75">A32</font></span></a>, <a class="ref" href="nat_d.html#T66" onmouseover="rs('nat_d/T66')" onmouseout="rh()">NAT_D:66</a></span>
<br/>.= 
4001 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2311 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4000</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T24" onmouseover="rs('nat_d/T24')" onmouseout="rh()">NAT_D:24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2310 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1691</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 2310
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:46"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
1691 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1691 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 619</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">619 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 453</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 619
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">453 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 166</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 453
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
166 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">166 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 121</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">121 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 45</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 121
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
45 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">45 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 31</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">31 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 14</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 31
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
14 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">14 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 3
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
2 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
2 <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="euler_1.html#T8" onmouseover="rs('euler_1/T8')" onmouseout="rh()">EULER_1:8</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T51" onmouseover="rs('newton/T51')" onmouseout="rh()">NEWTON:51</a></span>
;<br/>
<span class="lab"><font color="Green" title="E77">A34</font></span>: <span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 2048</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1024</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001

<br/>.= 
2268
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:46"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="txt" href="#E10:46"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="ref" href="nat_4.html#T11" target="_self" onmouseover="rs('nat_4/T11')" onmouseout="rh()">Th11</a></span>
;<br/>
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">4001 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">2048 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1952</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:46"><span class="lab"><font color="Green" title="E67">A24</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 2048</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1952</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 2048</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default">1024 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 928</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 1024</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 928</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:46"><span class="lab"><font color="Green" title="E77">A34</font></span></a>, <a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p0">(<span class="default">512 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 416</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:46"><span class="lab"><font color="Green" title="E74">A31</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 512</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 416</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 160</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:46"><span class="lab"><font color="Green" title="E73">A30</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 160</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default">128 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:46"><span class="lab"><font color="Green" title="E72">A29</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 128</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T8" onmouseover="rs('newton/T8')" onmouseout="rh()">NEWTON:8</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3441 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1823</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:46"><span class="lab"><font color="Green" title="E69">A26</font></span></a>, <a class="txt" href="#E36:46"><span class="lab"><font color="Green" title="E71">A28</font></span></a>, <a class="ref" href="nat_d.html#T67" onmouseover="rs('nat_d/T67')" onmouseout="rh()">NAT_D:67</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">1522 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3376</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:46"><span class="lab"><font color="Green" title="E63">A20</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">3906 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 988</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:46"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1023 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 2164</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:46"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default">2268 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1219</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 4001
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:46"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:46"><span class="lab"><font color="Green" title="E65">A22</font></span></a>, <a class="ref" href="nat_d.html#D2" onmouseover="rs('nat_d/D2')" onmouseout="rh()">NAT_D:def 2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E45:46"/>
4001 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E8:46"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E42:46"><span class="lab"><font color="Green" title="E76">A33</font></span></a>, <a class="ref" href="nat_4.html#T25" target="_self" onmouseover="rs('nat_4/T25')" onmouseout="rh()">Th25</a>, <a class="ref" href="pepin.html#T59" onmouseover="rs('pepin/T59')" onmouseout="rh()">PEPIN:59</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
