Powers of two weighted sum of the first p divided Bernoulli numbers modulo p

13 Jan 2020 Levaillant Claire

We show that, modulo some odd prime p, the powers of two weighted sum of the first p divided Bernoulli numbers equals 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 Abstract
No code implementations yet. Submit your code now

Categories


  • COMBINATORICS
  • NUMBER THEORY