Armin Straub
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A q-analog of Ljunggren's binomial congruence
dmtcs:2962 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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https://doi.org/10.46298/dmtcs.2962
A q-analog of Ljunggren's binomial congruenceConference paper
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.
Ji-Cai Liu, 2022, A variation of the q-Wolstenholme theorem, Annali di Matematica Pura ed Applicata (1923 -), 201, 4, pp. 1993-2000, 10.1007/s10231-022-01187-w.