Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even. what kind of proof did you use?

Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even.

m=2k-n, p=2l-n

Let m+n and n+p be even integers, thus m+n=2k and n+p=2l by definition of even

m+p = 2k-n + 2l-n substitution

= 2k+2l-2n

=2 (k+l-n)

=2x, where x=k+l-n ∈Z (integers)

Hence, m+p is even by direct proof.