Journal of Integer Sequences, Vol. 17 (2014), Article 14.8.8

Congruences Involving Sums of Ratios of Lucas Sequences


Evis Ieronymou
Department of Mathematics and Statistics
University of Cyprus
1687 Nicosia
Cyprus

Abstract:

Given a pair (Ut) and (Vt) 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.

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Received June 5 2014; revised versions received July 18 2014; August 1 2014; August 8 2014. Published in Journal of Integer Sequences, August 12 2014.

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