Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.7

Another Lucasnomial Generalization of Wolstenholme's Congruence


Christian Ballot
Département de Mathématiques et Informatique
Université de Caen-Normandie
F14032 Caen Cedex
France

Abstract:

If $p\ge5$ is a prime, then Wolstenholme's congruence stipulates that $\binom{2p-1}{p-1}\equiv1\pmod{p^3}$. New generalizations of this congruence to Lucasnomials $\pmod{U_p^2V_p/V_1}$ are given, where U and V are a pair of Lucas sequences.

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Received August 9 2019; revised version received December 19 2019; December 24 2019; March 11 2020. Published in Journal of Integer Sequences, March 17 2020.

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