Question 88
For positive integers $a,b$, define $a\ominus b=\frac{a-b}{\operatorname{gcd}(a,b)}$. Prove that for every integer $n\gt1$, $n$ is a prime power (that is, $n=p^k$ for a prime $p$ and a positive integer $k$) if and only if $\operatorname{gcd}(n,n\ominus m)=1$ for every positive integer $m\lt n$.