Thread: Getting started on proof with primes! Need guidance

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

When you're asked to prove that something is false, the best (and in practice, pretty much the only) way to accomplish it is by finding what's called a counter-example, that is, given an implication $\displaystyle A\Rightarrow B$, you pick an example such that $\displaystyle A$ is satisfied but $\displaystyle B$ is not. In this case, pick for instance $\displaystyle p=8$ and $\displaystyle n=4$.

Thanks Nyrox. I got so wrapped up with my material that even the obvious seems out of reach. Again many thanks...