reserve a,b,c,k,m,n for Nat;
reserve p for Prime;

theorem
  for x,y,z being Nat st x,y are_coprime & x|^2+y|^2 = z|^4 holds 7 divides x*y
  proof
    let x,y,z be Nat;
    assume
A1: x,y are_coprime;
    then x is odd or y is odd by NEWTON05:35;
    hence thesis by A1,Lm1;
  end;
