In mathematics, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and

(mathematics) With respect to an integer base b, with b > 1, a composite integer n such that bⁿ⁻¹ is congruent to one modulo n.

In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in a 1998 preprint and published in 2000.

A strong pseudoprime is a composite number that passes the Miller–Rabin primality test.

Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequence.