Euler-Jacobi pseudoprime

From Number
Jump to: navigation, search

Template:Base-relative pseudoprimality property

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.

Relation with other properties

Weaker properties

Other related properties