theorem
  for p be prime Nat, k be non zero Nat st k < p holds
    not p divides p|^2 - k|^2
  proof
    let p be prime Nat, k be non zero Nat;
    reconsider a = k-1 as Nat;
    p divides (p - (a+1))*(p + (a+1)) implies a+1 >= p by PSQ;
    hence thesis by NEWTON01:1;
  end;
