
theorem
  for a be even Integer, b be Integer, n be non zero Nat st
    a,b are_coprime holds b|^n + a|^n, b|^n - a|^n are_coprime
  proof
    let a be even Integer, b be Integer, n be non zero Nat such that
    A1: a,b are_coprime;
    A2: a|^n, b|^n are_coprime by A1,WSIERP_1:11;
    (a|^n + b|^n), (a|^n - b|^n) are_coprime by A2,SCP; then
    1 = (a|^n + b|^n) gcd -(b|^n - a|^n)
    .= (a|^n + b|^n) gcd (b|^n - a|^n) by NEWTON02:1;
    hence thesis;
  end;
