Linear recurrence relations for binomial coefficients modulo a prime

dc.creatorMattarei, Sandro
dc.date2005-11-16
dc.date.accessioned2026-07-07T09:33:50Z
dc.date.available2026-07-07T09:33:50Z
dc.descriptionWe 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<p-h. This hypothesis can be weakened to 2h\le k<p if we assume, in addition, that the characteristic polynomial of the relation does not have -1 as a root. We apply our results to recover a known bound for the number of points of a Fermat curve over a finite field.
dc.identifierhttps://arxiv.org/abs/math/0511417
dc.identifierhttp://arxiv.org/abs/math/0511417
dc.identifierJ. Number Theory 128 (2008), no. 1, 49-58
dc.identifierdoi:10.1016/j.jnt.2007.05.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159277
dc.subjectNumber Theory
dc.subject11B65; 05A10
dc.titleLinear recurrence relations for binomial coefficients modulo a prime
dc.typetext

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