Geodesic
Congruences involving sums of ratios of Lucas sequences
Journal of integer sequences, Tome 17 (2014) no. 8.

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, we establish various congruences involving sums of ratios $\frac{V_t}{U_t}$. More precisely, let $p$ be a prime divisor of the positive integer $m$. We establish congruences, modulo powers of $p$, for the sum $\sum \frac{V_t}{U_t}$, where $t$ runs from 1 to $r(m)$, the rank of $m$, and $r(q) \nmid t$ for all prime factors $q$ of $m$.
Classification : 11B39, 11A07
Keywords: Lucas sequence, rank of appearance, congruence 
@article{JIS_2014__17_8_a7,
     author = {Ieronymou, Evis},
     title = {Congruences involving sums of ratios of {Lucas} sequences},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {17},
     number = {8},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_8_a7/}
}
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Ieronymou, Evis. Congruences involving sums of ratios of Lucas sequences. Journal of integer sequences, Tome 17 (2014) no. 8. http://geodesic.mathdoc.fr/item/JIS_2014__17_8_a7/