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Congruences Involving Sums of Ratios of
Lucas Sequences Evis Ieronymou
Department of Mathematics and Statistics
University of Cyprus
1687 Nicosia
Cyprus
mailto:ieronymou.evis@ucy.ac.cyieronymou.evis@ucy.ac.cy

in

Abstract:

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.