Converse
The converse of Fermat's little theorem is not generally true, as it fails for Carmichael numbers. However, a slightly stronger form of the theorem is true, and is known as Lehmer's theorem. The theorem is as follows:
If there exists an a such that
and for all prime q dividing p − 1
then p is prime.
This theorem forms the basis for the Lucas–Lehmer test, an important primality test.
Read more about this topic: Fermat's Little Theorem
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