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.