Question

If a and b are odd integers, then a - b is an even integer

Answer 1

An even integer is a multiple of 2, such as 2n. An odd integer is a multiple of 2 + 1, such as 2m + 1. If you subtract two odd numbers, you end up with something like

\[2m + 1 - (2n + 1) = 2m + 1 - 2n - 1 = 2m - 2n\]Obviously, both 2m and 2n are even integers, and so the result of subtracting two odd integers is an even integer.