A q-analog of Ljunggren's binomial congruence

Armin Straub

A q-analog of Ljunggren's binomial congruence

Number Theory 2011-03-17 v1 Combinatorics

Authors: Armin Straub

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.

Keywords

q-analog binomial congruence Ljunggren congruence Wolstenholme congruence Babbage congruence Glaisher congruence

Cite

@article{arxiv.1103.3258,
  title  = {A q-analog of Ljunggren's binomial congruence},
  author = {Armin Straub},
  journal= {arXiv preprint arXiv:1103.3258},
  year   = {2011}
}

Comments

6 pages, to be published in the proceedings of FPSAC 2011

A q-analog of Ljunggren's binomial congruence

Abstract

Keywords

Cite

Comments

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