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# State/Computing the totient of a prime power

Proposition: (Computing the totient of a prime power) Suppose that $p$ is a prime number, and $n$ is a positive integer. Then the totient of $p^n$ can be computed with the following formula: $$\phi(p^n) = p^n - p^{n-1}.$$ In particular, $\phi(p) = p-1$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Totient, Def/Invertible residue, State/Uniqueness of prime factorization, State/Counting multiples of d between 1 and n

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