Good day to all,

I have asked to prove that the following statement is false:

if p is not prime and p|n^2 then p|n

My train of thoughts consisted of the following:

(1) Assume the statement is true and arrive at some contradiction.

(2) Since p is not prime then it is a composite number and can be expressed uniquely as a product of primes.

(3) Since we have assumed p|n^2 => n^2 = kp for some integer k

My problem lies in the fact that I am not quite sure how to merge my assumptions and arrive at some contradiction (if this is even the best method?). As I stated in the title I am not looking for an explicit answer but guidance, as I will learn nothing if someone just hands me the solution.

Thanks again