A Further Generalization of a Congruence of Wolstenholme

Christian Ballot L.M.N.O., CNRS UMR 6139 Université de Caen F-14032 Caen Cedex France

              christian.ballot@unicaen.fr

Abstract

Given a pair (U_{t}) and (V_{t}) of Lucas sequences, Kimball and Webb showed that ∑_{0<t<ρ_{U}} \frac{V_{t}}{U_{t}} ≡ 0 (mod p^{2}), if p is a prime ≥ 5 whose rank ρ_{U} is maximal, that is to say, ρ_{U} is p or p±1. We extend their result replacing p by a composite integer m of maximal rank, thereby providing a generalization of a classical congruence of Leudesdorf.