Let $b, k$, and $n$ be integers that satisfy $\gcd(b, n) = 1$ and $\gcd(k, \varphi(n)) = 1$. Show that $b$ has exactly one kth root modulo $n$.

Question

Let $b, k,$ and $n$ be integers that satisfy $\gcd(b, n) = 1$ and $\gcd(k, φ(n)) = 1$. Show that $b$ has exactly one $k^{\text{th}}$ root modulo $n$.