Definition
Fermat's little theorem states that if p is prime and a is coprime to p, then ap−1 − 1 is divisible by p. If a composite integer x is coprime to an integer a > 1 and x divides ax−1 − 1, then x is called a Fermat pseudoprime to base a. In other words, a composite integer is a Fermat pseudoprime to base a if it successfully passes Fermat primality test for the base a.
The smallest base-2 Fermat pseudoprime is 341. It is not a prime, since it equals 11·31, but it satisfies Fermat's little theorem: 2340 ≡ 1 (mod 341) and thus passes Fermat primality test for the base 2.
Pseudoprimes to base 2 are sometimes called Poulet numbers, Sarrus numbers, or Fermatians (sequence A001567 in OEIS).
An integer x that is a Fermat pseudoprime for all values of a that are coprime to x is called a Carmichael number.
Read more about this topic: Fermat Pseudoprime
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)