Congruences for $${\varvec{q}}$$-Binomial Coefficients

Annals of Combinatorics - Tập 23 Số 3-4 - Trang 1123-1135 - 2019
Wadim Zudilin1
1Department of Mathematics, IMAPP, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands

Tóm tắt

AbstractWe discussq-analogues of the classical congruence$$\left( {\begin{array}{c}ap\\ bp\end{array}}\right) \equiv \left( {\begin{array}{c}a\\ b\end{array}}\right) \pmod {p^3}$$apbpab(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.

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