Linear recurrence relations for binomial coefficients modulo a prime

Details Linear recurrence relations for binomial coefficients modulo a prime Linear recurrence relations for binomial coefficients modulo a prime

2005-11-16

arxiv.org/abs/math/0511417v1

J. Number Theory 128 (2008), no. 1, 49-58

Mathematics

Number Theory

Scientific paper

10.1016/j.jnt.2007.05.003

We investigate when the sequence of binomial coefficients \binom{k}{i} modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree h in the finite range 0\le i\le k. In particular, we prove that this cannot occur if 2h\le k

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