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.