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Fermat's Little Theorem Converse


The converse of Fermat's little theorem is also known as Lehmer's theorem. It states that, if an integer x is prime to m and x^(m-1)=1 (mod m) and there is no integer e<m-1 for which x^e=1 (mod m), then m is not prime. Here, x is called a witness to the primality of m. This theorem is the basis for the Pratt primality certificate.


See also

Fermat's Little Theorem, Pratt Certificate, Primality Certificate, Witness

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References

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, p. 96, 1994.Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 278-279, 1991.

Referenced on Wolfram|Alpha

Fermat's Little Theorem Converse

Cite this as:

Weisstein, Eric W. "Fermat's Little Theorem Converse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FermatsLittleTheoremConverse.html

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