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arXiv · 1901.07843

Congruences for $q$-binomial coefficients

Wadim Zudilin
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Abstract

We discuss $q$-analogues of the classical congruence $\binom{ap}{bp}\equiv\binom{a}{b}\pmod{p^3}$, valid for primes $p>3$, as well as its generalisations. In particular, we prove related congruences for ($q$-analogues of) integral factorial ratios.

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Wadim Zudilin. 2019-01-23. Congruences for $q$-binomial coefficients. https://doi.org/10.1007/s00026-019-00461-8

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