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.