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Euler's phi function

Euler's phi function $\phi$(n) is the size of Z*n = { \([a]_n \;\in\;
Z_n\): gcd(a,n) = 1}, the multiplicative group mod n. $\phi$(p) = p-1 if p is prime.



Euler's Theorem

For any integer n > 1, \(a^{\phi(n)} \;\equiv\; 1\) (mod n) for all \(a \in Z_n^{\ast}\).



Fermat's Theorem

If p is prime, then \(a^{p-1} \;\equiv\; 1\) (mod p) for all \(a \in Z_p^{\ast}\).


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