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## Homework Statement

Let n be an integer. Prove that if n^3 is even, then n is even.

## Homework Equations

## The Attempt at a Solution

Suppose n is even. That is n=2m, for some mεZ.

Then, n^3=(2m)^3=8m^3=2(4m^3).

Since 4m^3 is an integer, n^3 will be even.

Now, i proved that if n is even, then n^3 is even. So would this be a valid proof in this context?