Euler pseudoprime: Difference between revisions
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== Further reading == | == Further reading == | ||
* [[Richard E. Crandall]] and [[Carl Pomerance]]. Prime Numbers: A Computational Perspective. Springer-Verlag, 2001, ISBN 0-387-25282-7 | * [[Richard E. Crandall]] and [[Carl Pomerance]]. Prime Numbers: A Computational Perspective. Springer-Verlag, 2001, ISBN 0-387-25282-7 | ||
* [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5 | * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5[[Category:Suggestion Bot Tag]] |
Latest revision as of 07:00, 14 August 2024
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A composite number n is called an Euler pseudoprime to a natural base a if or
Properties
- Every Euler pseudoprime is odd.
- Every Euler pseudoprime is also a Fermat pseudoprime:
- and
- Every Euler Pseudoprime to base a that satisfies is an Euler-Jacobi pseudoprime.
- Strong pseudoprimes are Euler pseudoprimes too.
Absolute Euler pseudoprime
An absolute Euler pseudoprime is a composite number c that satisfies the congruence or for every base a that is coprime to c. Every absolute Euler pseudoprime is also a Carmichael number.
Further reading
- Richard E. Crandall and Carl Pomerance. Prime Numbers: A Computational Perspective. Springer-Verlag, 2001, ISBN 0-387-25282-7
- Paulo Ribenboim. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5