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.
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.