Geodesic
Congruences involving sums of ratios of Lucas sequences
Journal of integer sequences, Tome 17 (2014) no. 8
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},
     year = {2014},
     volume = {17},
     number = {8},
     zbl = {1358.11028},
     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/