Journal of Integer Sequences, Vol. 15 (2012), Article 12.8.6

A Further Generalization of a Congruence of Wolstenholme

Christian Ballot
L.M.N.O., CNRS UMR 6139
Université de Caen
F14032 Caen Cedex


Given a pair (Ut) and (Vt) of Lucas sequences, Kimball and Webb showed that $\sum_{0t\rho_U}\frac{V_t}{U_t} \equiv 0$ (mod p2), if p is a prime $\ge5$ whose rank $\rho_U$ is maximal, that is to say, $\rho_U$ is p or $p\pm1$. We extend their result replacing p by a composite integer m of maximal rank, thereby providing a generalization of a classical congruence of Leudesdorf.

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Received June 6 2012; revised version received October 8 2012. Published in Journal of Integer Sequences, October 8 2012.

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