Question

Gemme makes a conjecture that the sum of an odd integer and itself is always an even interger

Answer 1

It's true - all whole numbers that are odd are going to add up to an even integer. An odd integer can be looked at as an even number plus one. For example, 21 would be 20 (the even number) plus one. So the addition of two odd integers is like saying two even numbers were added to each other (in that example, 20 + 20), and then adding the 1+1 that made them odd (which adds up to 2, an even number). So it would be [20 + 20 + (1 + 1)]