A composite number n is called an Euler pseudoprime to a natural base a if or
- 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.