Let A be an odd number, B another odd number A = 2c + 1, B = 2d + 1 (where both c and d are integers) A - B = (2c + 1) - (2d + 1) = 2c-2d + (1-1) = 2(c+d) Since c and d are integers, c+d is an integer too, and A-B is even (since it can be expressed as 2*integer).