Armin Straub — Discrete Mathematics and Theoretical Computer Science — Special volume for FPSAC 2011 — 2011, Pages 897-902
Abstract
We prove a \(q\)-analog of a classical binomial congruence due to Ljunggren which states that \[ \binom{a p}{b p} \equiv \binom{a}{b} \] modulo \(p^3\) for primes \(p\ge5\). This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing \(q\)-analogs. Our congruence generalizes an earlier result of Clark.http://dmtcs.episciences.org/2962
Download
| Link | Size | Description | Hits |
|---|---|---|---|
| qljunggren.pdf | 299.34 KB | Preprint (PDF, 6 pages) | 3803 |
BibTeX
@article{qljunggren-2011,
author = {Armin Straub},
title = {A $q$-analog of {L}junggren's binomial congruence},
journal = {Discrete Mathematics and Theoretical Computer Science},
year = {2011},
pages = {897--902},
}