Show that the sum of any two odd numbers is even.

Hi here's a way to solve it

Let m and n be odd integers. Then, we can express m as 2r + 1 and n as 2s + 1, where r and s are integers.

This means that any odd number can be written as the sum of some even integer and one.

Substituting, we have that m + n = (2r + 1) + 2s + 1 = 2r + 2s + 2.

As we defined r and s as integers, 2r + 2s + 2 is also an integer.

Now It is clear that 2r + 2s + 2 is an integer divisible by 2 becasue we have 2 in each of the integers.

Therefore, 2r + 2s + 2 = m + n is even.

So, the sum of two odd integers is even.