- #1

cmajor47

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## Homework Statement

Prove that for all integers n and m, if n-m is even then n

^{3}-m

^{3}is even.

## Homework Equations

Definition of even: n=2k

## 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

n

^{3}-m

^{3}=(2k+m)

^{3}-(-2k+n)

^{3}

I did all of this algebra out but I didn't think that it worked in showing that n

^{3}-m

^{3}is even. Am I doing the proof wrong?