# Congruences involving binomial coefficients and Lucas sequences - Mathematics > Number Theory

Abstract: In this paper we obtain some congruences involving central binomialcoefficients and Lucas sequences. For example, we show that if p>5 is a primethen $\sum {k=0}^{p-1}F k*binom2k,k-12^k$ is congruent to 0,1,-1 modulo paccording 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.

Author: Zhi-Wei Sun

Source: https://arxiv.org/