Linear recurrence relations for binomial coefficients modulo a prime |
| |
Authors: | Sandro Mattarei |
| |
Institution: | Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy |
| |
Abstract: | We investigate when the sequence of binomial coefficients modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree h in the finite range 0?i?k. In particular, we prove that this cannot occur if 2h?k<p−h. This hypothesis can be weakened to 2h?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. |
| |
Keywords: | primary 11B65 secondary 05A10 |
本文献已被 ScienceDirect 等数据库收录! |
|