Divisibility of Power Sums and the Generalized Erdos-Moser Equation

Details Divisibility of Power Sums and the Generalized Erdos-Moser Equation Divisibility of Power Sums and the Generalized Erdos-Moser Equation

2010-10-12

arxiv.org/abs/1010.2275v4

Mathematics

Number Theory

4 pages, simplified proof of Proposition 1, added reference [4]

Scientific paper

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.

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