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

Department of Mathematics and Statistics

University of Cyprus

1687 Nicosia

Cyprus

**Abstract:**

Given a pair (*U*_{t}) and (*V*_{t}) of Lucas sequences,
we establish various congruences involving sums of ratios
.
More precisely, let *p* be a prime divisor of the positive integer *m*. We establish congruences, modulo powers of *p*, for the sum
,
where *t* runs from 1 to *r*(*m*), the rank of *m*, and
for all prime factors *q* of *m*.

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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