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On the Sum of Digits of Numerators of Bernoulli Numbers

Published:2012-02-03
Printed: Dec 2013
• Attila Bérczes,
Institute of Mathematics, University of Debrecen, Number Theory Research Group, Hungarian Academy of Sciences, Debrecen, Hungary
• Florian Luca,
Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
 Format: LaTeX MathJax PDF

Abstract

Let $b\gt 1$ be an integer. We prove that for almost all $n$, the sum of the digits in base $b$ of the numerator of the Bernoulli number $B_{2n}$ exceeds $c\log n$, where $c:=c(b)\gt 0$ is some constant depending on $b$.
 Keywords: Bernoulli numbers, sums of digits
 MSC Classifications: 11B68 - Bernoulli and Euler numbers and polynomials

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