What would you like to understand?

To derive $\varphi(p^k)$, we count the integers from 1 to $p^k$ that are coprime to $p^k$. An integer is not coprime to $p^k$ if and only if it shares a prime factor with $p^k$.

Conditions: $p$ is a prime number.; $k$ is a positive integer (implied by context).; The counting range is from 1 to $p^k$ inclusive.

To derive $\varphi(p^k)$, we count the integers from 1 to $p^k$ that are coprime to $p^k$. An integer is not coprime to $p^k$ if and only if it shares a prime factor with $p^k$.

Conditions: $p$ is a prime number.; $k$ is a positive integer (implied by context).; The counting range is from 1 to $p^k$ inclusive.