# 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!