## 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.

### MSC:

 11B65 Binomial coefficients; factorials; $$q$$-identities 05A10 Factorials, binomial coefficients, combinatorial functions 11A07 Congruences; primitive roots; residue systems
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### References:

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