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Problem

Here's \emph{Euler's $\phi$-function}: $\phi(n)$ counts the numbers between 1 and $n$ that are relatively prime to $n$.
Compute the first couple of values of this function: $\phi(1), \phi(2), \phi(3), \dots$
Find a formula for $\phi(n)$ when $n$ is prime.
Find a formula for $\phi(mn)$ in terms of $\phi(m)$ and $\phi(n)$ in the case that $m$ and $n$ are relatively prime.
One of Euler's theorem says that, if $a$ is relatively prime to $n$, then $a^{ \phi(n) } \equiv 1 \bmod n$.
Conclude that, if $b \cdot c \equiv 1 \bmod \phi(n)$, then $\left( a^b \right)^c \equiv a \bmod n$.

Details
Contributer: Matt
Authors
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References
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Problem Sets This Problem Belongs to:
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VARIABLES
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DEFINITIONS
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