On the pseudoprimes of the form ax + b

Abstract

A composite number n is called a pseudoprime if n|2n− 2.Theorem 1. If a and b are natural numbers such that (a, b) = 1, then there exist infinitely many pseudoprimes of the form ax + b, where x is a natural number.The proof of this theorem is given by the author in (5). This proof is based on the following two lemmas.