Congruences for \(q\)-binomial coefficients. (English) Zbl 1431.11032

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


11B65 Binomial coefficients; factorials; \(q\)-identities
05A10 Factorials, binomial coefficients, combinatorial functions
11A07 Congruences; primitive roots; residue systems
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