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More Congruences for Central Binomial Sums
with Fibonacci and Lucas Numbers Roberto Tauraso
Dipartimento di Matematica
Università di Roma Tor Vergata
00133 Roma
Italy
tauraso@mat.uniroma2.it

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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.