group theory – If $(h,k) = 1$, then $h^{phi(k)}equiv 1(textrm{mod} k)$?

I have encountered a statement which says: for natural numbers $h$ and $k$ such that $(h,k)=1$,we will have $h^{phi(k)}equiv 1(textrm{mod} k)$, where $phi(k)$ is the Euler’s totient function that shows the number of positive integers not exceeding $k$ relatively prime to $k$. I wonder is there any formal theorems that illustrate this statement? And how will this theorem be proved?

I think this statement is related closely with cyclic group in group theory, but I can’t think of any useful facts to prove this statement. Thank you very much in advance for any replies!