reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve c for Complex;

theorem
  2 = 1|^4+1|^4 & 17 = 1|^4+2|^4 & 97 = 2|^4+3|^4 &
  257 = 1|^4+4|^4 & 641 = 2|^4+5|^4
  proof
A1: 2|^4 = 2*2*2*2 by POLYEQ_5:3;
A2: 3|^4 = 3*3*3*3 by POLYEQ_5:3;
A3: 4|^4 = 4*4*4*4 by POLYEQ_5:3;
A4: 5|^4 = 5*5*5*5 by POLYEQ_5:3;
    thus 2 = 1|^4+1|^4;
    thus 17 = 1|^4+2|^4 by A1;
    thus 97 = 2|^4+3|^4 by A1,A2;
    thus 257 = 1|^4+4|^4 by A3;
    thus 641 = 2|^4+5|^4 by A1,A4;
  end;
