1. The problem statement, all variables and given/known data Prove that for all integers n and m, if n-m is even then n3-m3 is even. 2. Relevant equations Definition of even: n=2k 3. The attempt at a solution Proof: Let n, m [tex]\in[/tex] Z such that n-m=2k n-m=2k n=2k+m m=-2k+n n3-m3=(2k+m)3-(-2k+n)3 I did all of this algebra out but I didn't think that it worked in showing that n3-m3 is even. Am I doing the proof wrong?