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


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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