Euler pseudoprime

Definition

Suppose $n$ is a composite natural number and $a$ is a natural number relatively prime to $n$. We say that $n$ is an Euler pseudoprime to base $a$ if $n$ is odd, and:

$a^{(n-1)/2}\equiv \pm 1{\pmod {n}}$.

Relation with other properties

Stronger properties

• Strong pseudoprime
• Euler-Jacobi pseudoprime

Weaker properties

• Fermat pseudoprime