Fermat's Little Theorem

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If ${a}$ is an integer and ${p}$ is a prime number, then $a^{p-1}\equiv 1 \pmod {p}$.

Note: This theorem is a special case of Euler's totient theorem.


A frequently used corolary of Fermat's little theorem is $a^p \equiv a \pmod {p}$. As you can see, it is derived by multipling both sides of the theorem by a.


This theorem is credited to Pierre Fermat.

See also