A congruence concerning a convolution involving weighted Bernoulli numbers

Abstract

Given a prime $p\ge 5$, we reduce modulo p a convolution of order p-1 of powers of two weighted Bernoulli numbers with Bernoulli numbers in terms of harmonic numbers and generalized harmonic numbers. Our proof is based on studying the p-adic expansion of the number of permutations of Sym(p-2) with an even number of ascents, up to the modulus $p^2$.

12 pages, 22 references

References in corpus (2)

• Powers of two weighted sum of the first p divided Bernoulli numbers modulo p
• Congruences related to Miki's identity