Concept
Fermat's little theorem states that if p is prime and, then
If we want to test if p is prime, then we can pick random a's in the interval and see if the equality holds. If the equality does not hold for a value of a, then p is composite. If the equality does hold for many values of a, then we can say that p is probable prime.
It might be in our tests that we do not pick any value for a such that the equality fails. Any a such that
when n is composite is known as a Fermat liar. Vice versa, in this case n is called Fermat pseudoprime to base a.
If we do pick an a such that
then a is known as a Fermat witness for the compositeness of n.
Read more about this topic: Fermat Primality Test
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