Powers of two weighted sum of the first p divided Bernoulli numbers modulo p
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).
PDF AbstractCategories
Combinatorics
Number Theory
05A05, 05A19, 11Y11, 11Y40
G.2.1
