# A $q$-analog of Ljunggren's binomial congruence

Abstract : We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that $\binom{ap}{bp} \equiv \binom{a}{b}$ modulo $p^3$ for primes $p \geq 5$. 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.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [10 references]

https://hal.inria.fr/hal-01215062
Contributor : Coordination Episciences Iam <>
Submitted on : Tuesday, October 13, 2015 - 3:05:55 PM
Last modification on : Friday, August 2, 2019 - 11:52:02 AM
Long-term archiving on: : Thursday, April 27, 2017 - 12:14:15 AM

### File

dmAO0178.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01215062, version 1

### Citation

Armin Straub. A $q$-analog of Ljunggren's binomial congruence. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.897-902. ⟨hal-01215062⟩

Record views