# Euler-Jacobi pseudoprime

From Number

Template:Base-relative pseudoprimality property

## Contents

## Definition

Let be a composite natural number and be an integer relatively prime to . We say that is an **Euler-Jacobi pseudoprime** with respect to the base if is odd and:

,

where the expression on the right is the Jacobi symbol of mod . Note that the analogous statement *is* true for all primes, because for a prime, the Jacobi symbol equals the Legendre symbol.