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Congruences for $${\varvec{q}}$$q -Binomial Coefficients
Annals of Combinatorics ( IF 0.6 ) Pub Date : 2019-11-11 , DOI: 10.1007/s00026-019-00461-8
Wadim Zudilin

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

中文翻译:

$$ {\ varvec {q}} $$ q的同余项-二项式系数

我们讨论q古典一致性的-analogues \(\左({\ {开始}阵{C} AP \\ BP \ {结束阵列}} \右)\当量\左({\ {开始}阵{C} a \\ b \ end {array}} \ right)\ pmod {p ^ 3} \),用于质数\(p> 3 \)及其推广。特别地,我们证明了整数阶乘比的(q-模拟)的相关同余。
更新日期:2019-11-11
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