Prove or disprove : if $x|y^2 $then $x|y$ How can I prove such statement?
I think that if $x|y^2$ then $x|(y*y)$ so $x|y$ or $x|y$ which means that in any case $x|y$. Am I correct?
I ask this question as such template because I think that it doesn't matter which $x$ or $y$ represents.
However, the original question is: if $6|n^2$ then $6|n$ and if $12|n^2$ then $12|n$.

Hint $\ $ It fails for $\,x = y^2 > 1.\ $ It is true iff $x$ is squarefree.
