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Famous Theorems of Mathematics/Fermat's little theorem

< Famous Theorems of Mathematics

Fermat's little theorem (not to be confused with Fermat's last theorem) states that if is a prime number, then for any integer , will be evenly divisible by . This can be expressed in the notation of modular arithmetic as follows:

A variant of this theorem is stated in the following form: if is a prime and is an integer coprime to , then will be evenly divisible by . In the notation of modular arithmetic: