Congruences Involving Sums of Ratios of Lucas Sequences

Evis Ieronymou
2014 Journal of Integer Sequences   unpublished
Given a pair (U t) and (V t) of Lucas sequences, we establish various congruences involving sums of ratios Vt Ut. More precisely, let p be a prime divisor of the positive integer m. We establish congruences, modulo powers of p, for the sum Vt Ut , where t runs from 1 to r(m), the rank of m, and r(q) ∤ t for all prime factors q of m.