Combinatorial Sums $\sum_{k\equiv r(\mbox{mod } m)}{n\choose k}a^k$ and Lucas Quotients

Jiangshuai Yang; Yingpu Deng

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arXiv · 1606.08245

Combinatorial Sums $\sum_{k\equiv r(\mbox{mod } m)}{n\choose k}a^k$ and Lucas Quotients

Jiangshuai Yang·Yingpu Deng

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Abstract

In this paper, we study the combinatorial sum $$\sum_{k\equiv r(\mbox{mod }m)}{n\choose k}a^k.$$ By studying this sum, we obtain new congruences for Lucas quotients of two infinite families of Lucas sequences. Only for three Lucas sequences, there are such known results.

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Jiangshuai Yang, Yingpu Deng. 2016-06-27. Combinatorial Sums $\sum_{k\equiv r(\mbox{mod } m)}{n\choose k}a^k$ and Lucas Quotients. https://arxiv.org/abs/1606.08245

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