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A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy.
Fermat pseudoprimes
Fermat's little theorem states that if p is prime and a is coprime to p, then a^{p−1} − 1 is divisible by p. If a composite integer x is coprime to an integer a > 1 and x divides a^{x−1} − 1, then x is called a Fermat pseudoprime to base a. Some sources use variations of this definition, for example to only allow odd numbers to be pseudoprimes.^{[1]}
An integer x that is a Fermat pseudoprime to all values of a that are coprime to x is called a Carmichael number.
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