A Study of the nersenne Numbers

Abstract

The purpose of this paper is, as the title suggests, to study the Mersenne numbers. This topic was chosen for, to my knowledge, there exist few papers which deal exclusively with the Mersenne numbers. Rather, there exist many isolated results in numerous books. This paper, then, is a collection of these known results as well as several original ones. The approach is historical as the paper is divided into four main parts which are arranged chronologically. They include a motivation for study, this being the perfect numbers, and the works of Fermat, Euler, and Lucas.