A q-analog of Ljunggren's binomial congruence

Details A q-analog of Ljunggren's binomial congruence A q-analog of Ljunggren's binomial congruence

2011-03-16

arxiv.org/abs/1103.3258v1

Mathematics

Number Theory

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

Scientific paper

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.

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