A q-analog of Ljunggren's binomial congruence

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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