(((((a |^ n) + (b |^ n)) * ((a |^ m) + (b |^ m))) + (((a |^ m) - (b |^ m)) * ((a |^ n) - (b |^ n)))) / 2) * 2 = ((a |^ (n + m)) + (b |^ (n + m))) * 2 by NEWTON01:8;
hence not (((a |^ n) + (b |^ n)) * ((a |^ m) + (b |^ m))) + (((a |^ m) - (b |^ m)) * ((a |^ n) - (b |^ n))) is odd ; :: thesis: verum