AbstractWe discussq-analogues of the classical congruence$$\left(
{\begin{array}{c}ap\\ bp\end{array}}\right) \equiv \left( {\begin{array}{c}a\\
b\end{array}}\right) \pmod {p^3}$$apbp≡ab(modp3), for primes$$p>3$$p>3, as well
as its generalisations. In particular, we prove related congruences for
(q-analogues of) integral factorial ratios.