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.