Linear recurrence relations for binomial coefficients modulo a prime
| dc.creator | Mattarei, Sandro | |
| dc.date | 2005-11-16 | |
| dc.date.accessioned | 2026-07-07T09:33:50Z | |
| dc.date.available | 2026-07-07T09:33:50Z | |
| dc.description | 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<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.identifier | https://arxiv.org/abs/math/0511417 | |
| dc.identifier | http://arxiv.org/abs/math/0511417 | |
| dc.identifier | J. Number Theory 128 (2008), no. 1, 49-58 | |
| dc.identifier | doi:10.1016/j.jnt.2007.05.003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159277 | |
| dc.subject | Number Theory | |
| dc.subject | 11B65; 05A10 | |
| dc.title | Linear recurrence relations for binomial coefficients modulo a prime | |
| dc.type | text |