# Euler pseudoprime

From Citizendium

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