Prime factors of A^(m)-1 and A^(n)-1

Abstract

There are some of the sets of prime factors of A^(n)-1 with A, n in the set of all positive integers. Especially, in the case , the numbers of the form 2^(n)-1 are called Mersenne numbers. In general, A^(m)-1 and A^(n)-1 have the same prime factors when A,m,n are positive integers and A>1. In the thesis, we prove adding precise details about properties of prime factors of A^(m)-1 and A^(n)-1 using some Theorem and Lemma, and then show several Examples.