Generalization of "If $p$ is an integer and $p^2$ is even then $p$ is even" The statement in the title is true.
I am just wondering if a general statement of the the above statement which I state below is true.

Proposition: If $p$ is an integer and $n$ divides $p^2$ then $n$ divides $p$. 


There is a generalization: if $p$ is an integer and $n$ is prime, then if $n$ divides $p^2$, we have that $n$ divides $p$. This is obvious when you examine the prime factorization of $p$. 
