Congruences involving binomial coefficients and Lucas sequences

Details Congruences involving binomial coefficients and Lucas sequences Congruences involving binomial coefficients and Lucas sequences

2009-12-07

arxiv.org/abs/0912.1280v5

Mathematics

Number Theory

23 pages. The current Th. 1.4 is new

Scientific paper

In this paper we obtain some congruences involving central binomial
coefficients and Lucas sequences. For example, we show that if p>5 is a prime
then $\sum_{k=0}^{p-1}F_k*binom(2k,k)/12^k$ is congruent to 0,1,-1 modulo p
according as p=1,4 (mod 5), p=13,17 (mod 30), and p=7,23 (mod 30) respectively,
where {F_n} is the Fibonacci sequence. We also raise several conjectures.

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