Geodesic
On a congruence of Kimball and Webb involving Lucas sequences
Journal of integer sequences, Tome 17 (2014) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Given a pair $(U_{t})$ and $(V_{t})$ of Lucas sequences, an odd integer $\nu\ge1$, and a prime $p\ge\nu+4$ of maximal rank $\rho_U$, i.e., such that $\rho_U$ is $p$ or $p\pm1$, we show that $\sum_{0t\rho_U}(V_t/U_t)^\nu \equiv0\pmod{p^2}$. This extends a result of Kimball and Webb, who proved the case $\nu=1$. Some further generalizations are also established.
Classification : 11B39, 11A07
Keywords: Lucas sequence, rank of appearance, congruence, Wolstenholme, leudesdorf 
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     author = {Ballot, Christian},
     title = {On a congruence of {Kimball} and {Webb} involving {Lucas} sequences},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a0/}
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Ballot, Christian. On a congruence of Kimball and Webb involving Lucas sequences. Journal of integer sequences, Tome 17 (2014) no. 1. http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a0/