A Theorem involving the denominators of Bernoulli numbers
Number Theory
2013-10-01 v1
Abstract
Consider the average of the first n k-th powers. We pose and answer the following natural question: For which values of n and k is this average an integer? If k is odd the answer is easy; it is an integer as long as n is incongruent to 2 modulo 4. If k is even then the criterion involves the denominator of the k-th Bernoulli number. The average is an integer iff is not divisible by any prime which divides the denominator of the k-th Bernoulli number.
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Cite
@article{arxiv.1309.7751,
title = {A Theorem involving the denominators of Bernoulli numbers},
author = {Pantelis A. Damianou and Peter Schumer},
journal= {arXiv preprint arXiv:1309.7751},
year = {2013}
}
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6 pages