Journal of Integer Sequences, Vol. 26 (2023), Article 23.8.3

More Congruences for Central Binomial Sums with Fibonacci and Lucas Numbers


Roberto Tauraso
Dipartimento di Matematica
Università di Roma Tor Vergata
00133 Roma
Italy

Abstract:

We mainly determine $\sum_{k=1}^{p-1}\binom{2k}{k}h_kx^k$ modulo a prime $p$ with $h_k=\sum_{j=1}^k\frac{1}{2j-1}$. We also provide some applications of this polynomial congruence for some special values of $x$ which involve the Fibonacci and Lucas numbers.
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(Concerned with sequences A000032 A000045 A001254 A099921.)

Received June 17 2023; revised versions received June 18 2023; October 1 2023; October 2 2023. Published in Journal of Integer Sequences, October 3 2023.

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