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

theorem
  for k being Integer holds (2*k - 1) gcd (9*k + 4) = (k + 8) gcd 17
  proof
    let k be Integer;
    thus (2*k - 1) gcd (9*k + 4) = (2*k - 1) gcd ((9*k + 4) - 4*(2*k - 1))
    by NEWTON02:5
    .= ((2*k - 1) - 2*(k + 8)) gcd (k + 8) by NEWTON02:5
    .= (-17) gcd (k + 8)
    .= (k + 8) gcd 17 by NEWTON02:1;
  end;
