1. Prove that if an integer n is a perfect square, then n + 2 is not a perfect square.

Below is what I have so far. I need help completing it.

Method: Proof by Contradiction

Theorem: If n is a perfect square, then n + 2 is not a perfect square.

Proof:

Suppose n and n+2 are perfect squares.

Therefore, they can be written as n = k2 and n + 2 = m2 for some positive integers k and m.

2.

Prove that there is no largest rational negative number.

Method: Proof by Contradiction

Theorem: There is no largest rational negative number.

Proof.