Question: prove the product of two odd integers is odd?
Answer: So two odd numbers can be represented by 2a +1 and 2b +1, the product would be: (2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x. So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.