Modular periodicity of binomial coefficients
| dc.creator | Mattarei, Sandro | |
| dc.date | 2005-10-05 | |
| dc.date | 2006-11-23 | |
| dc.date.accessioned | 2026-07-07T06:47:10Z | |
| dc.date.available | 2026-07-07T06:47:10Z | |
| dc.description | We prove that if the signed binomial coefficient $(-1)^i\binom{k}{i}$ viewed modulo p is a periodic function of i with period h prime to p in the range $0\le i\le k$, then k+1 is a power of p, provided h is not too large compared to k. (In particular, $2h\le k$ suffices.) As an application, we prove that if G and H are multiplicative subgroups of a finite field, with H<G, and such that $1-α\in G$ for all $α\in G\setminus H$, then $G\cup\{0\}$ is a subfield. | |
| dc.description | 8 pages. Somehow, the references were missing in the previous version. An error in the abstract (but not in the main text) of the printed version is corrected here: h needs to be prime to p | |
| dc.identifier | https://arxiv.org/abs/math/0510100 | |
| dc.identifier | http://arxiv.org/abs/math/0510100 | |
| dc.identifier | Journal of Number Theory 117 (2006), no. 2, 471-481 | |
| dc.identifier | doi:10.1016/j.jnt.2005.07.005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103569 | |
| dc.subject | Number Theory | |
| dc.subject | 11B65; 05A10 | |
| dc.title | Modular periodicity of binomial coefficients | |
| dc.type | text |