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\vskip 1cm{\LARGE\bf Congruences Involving Sums of Ratios of  \\
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Lucas Sequences
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\large
Evis Ieronymou \\
Department of Mathematics and Statistics\\
University of Cyprus \\
1687 Nicosia \\
Cyprus \\
\href{mailto:ieronymou.evis@ucy.ac.cy}{\tt ieronymou.evis@ucy.ac.cy}
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\begin{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 $m$.
\end{abstract}


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