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## Homework Statement

Prove that p^2 is a mutiple of 3 ⇔ p is a multiple of 3. We are told p is an integer.

## The Attempt at a Solution

If p is a multiple of 3 then p=3.a (aEZ) and p^2 = 3.(3.a^2) which is clearly a multiple of 3

Suppose p^2 is a multiple of 3.

Then P^2 = 3.a and p=3.(√a/√3) since we know p is an interger (√a/√3) must be an integer and therefore p is a multiple of 3.

## Homework Equations

This isn't the solution that was given to me and I'm wondering whether it is correct or if I've missed something obvious. Or if there is an even easier way to do it.