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Armin Straub - 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) - https://doi.org/10.46298/dmtcs.2962
A q-analog of Ljunggren's binomial congruenceConference paper

Authors: Armin Straub ORCID1

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.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: q-analogs,binomial coefficients,binomial congruence,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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