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<span class="kw">let </span><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">l</font> be   <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>   <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2</span><br/>

<a NAME="E1:36"/>
( 1 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> 2 is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  &amp; <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 is  <a href="abian.html#V1" title="ABIAN:attr.1">odd</a>  &amp; 1 is  <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>  )
 
;<br/>
<a NAME="E2:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A1</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton05.html#T22" target="_self" onmouseover="rs('newton05/T22')" onmouseout="rh()">N0319</a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T66" onmouseover="rs('nat_d/T66')" onmouseout="rh()">NAT_D:66</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">2 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8</span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> 8
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T66" onmouseover="rs('nat_d/T66')" onmouseout="rh()">NAT_D:66</a>, <a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>
<br/>.= 
2 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>
<br/>.= 
2

;<br/>
<span class="kw">hence </span><a NAME="E4:36"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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/>


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