reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for a,b be odd square Nat holds 8 divides a - b
proof
  let a,b be odd square Nat;
  consider c such that
  A1: a = c^2 by PYTHTRIP:def 3;
  consider d such that
  A2: b = d^2 by PYTHTRIP:def 3;
  c is odd & d is odd & a = c|^2 & b = d|^2 by A1,A2;
  hence thesis by NEWTON02:63;
end;
