Powers of two weighted sum of the first p divided Bernoulli numbers modulo p
Combinatorics
2021-11-08 v4 Number Theory
Abstract
We show that, modulo some odd prime p, the powers of two weighted sum of the first p-2 divided Bernoulli numbers equals the Agoh-Giuga quotient plus twice the number of permutations on p-2 letters with an even number of ascents and distinct from the identity. We provide a combinatorial characterization of Wieferich primes, as well as of primes p for which p^2 divides the Fermat quotient q_p(2).
Keywords
Cite
@article{arxiv.2001.03471,
title = {Powers of two weighted sum of the first p divided Bernoulli numbers modulo p},
author = {Claire Levaillant},
journal= {arXiv preprint arXiv:2001.03471},
year = {2021}
}
Comments
26 pages, 24 references; new version: typo in equation numbering corrected