On a special congruence of Carlitz
| dc.creator | Mattarei, Sandro | |
| dc.date | 2006-02-01 | |
| dc.date.accessioned | 2026-07-07T07:03:00Z | |
| dc.date.available | 2026-07-07T07:03:00Z | |
| dc.description | We prove that if $q$ is a power of a prime $p$ and $p^k$ divides $a$, with $k\ge 0$, then \[ 1+(q-1)\sum_{0\le b(q-1)<a} \binom{a}{b(q-1)}\equiv 0\pmod{p^{k+1}}. \] The special case of this congruence where $q=p$ was proved by Carlitz in 1953 by means of rather deep properties of the Bernoulli numbers. A more direct approach produces our generalization and several related results. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602012 | |
| dc.identifier | http://arxiv.org/abs/math/0602012 | |
| dc.identifier | Integers 6 (2006), A09, 13 pp. (electronic) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108812 | |
| dc.subject | Number Theory | |
| dc.subject | 11B65 (Primary); 05A10, 05A19, 11A07 (Secondary) | |
| dc.title | On a special congruence of Carlitz | |
| dc.type | text |