A q-analog of Ljunggren's binomial congruence

This article by Armin Straub has been published in Proceedings of FPSAC 2011 .

You can also find this article on the arXiv as 1103.3258v1 [math.NT].

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 p3 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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