Divisibility of Power Sums and the Generalized Erdos-Moser Equation
Number Theory
2012-11-27 v4
Abstract
Using elementary methods, we determine the highest power of 2 dividing a power sum 1^n + 2^n + . . . + m^n, generalizing Lengyel's formula for the case where m is itself a power of 2. An application is a simple proof of Moree's result that, if (a,m,n) is any solution of the generalized Erdos-Moser Diophantine equation 1^n + 2^n + . . . + (m-1)^n = am^n, then m is odd.
Keywords
Cite
@article{arxiv.1010.2275,
title = {Divisibility of Power Sums and the Generalized Erdos-Moser Equation},
author = {Kieren MacMillan and Jonathan Sondow},
journal= {arXiv preprint arXiv:1010.2275},
year = {2012}
}
Comments
4 pages, simplified proof of Proposition 1, added reference [4]