A Theorem involving the denominators of Bernoulli numbers

Pantelis A. Damianou; Peter Schumer

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arXiv · 1309.7751

A Theorem involving the denominators of Bernoulli numbers

Pantelis A. Damianou·Peter Schumer

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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 $n$ is not divisible by any prime which divides the denominator of the k-th Bernoulli number.

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Pantelis A. Damianou, Peter Schumer. 2013-09-30. A Theorem involving the denominators of Bernoulli numbers. https://arxiv.org/abs/1309.7751

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