Let $p$ be prime, $a$ an integer, $(a,p)=1$ and $n$ a positive integer $(n,p-1)=1$. Prove $x^n\equiv a$ mod $p$ has a unique solution.
Take $G$ to be a group of order $600$. Prove that for any element a in $G$ there exist a $b$ in $G$ such that $a = b^7$