A Theorem Involving the Denominators of Bernoulli Numbers
Pantelis A. Damianou, Peter D. Schumer · Mathematics Magazine · 2003
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.