English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Suppose that $p$ is an odd prime and $m$ is an integer not divisible by $p$.Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave$\sum_{k=0}^{n-1}\binom{2k}{k+d}/m^k$ and$\sum_{k=0}^{n-1}\binom{2k}{k+d}/(km^k)$ modulo $p$ for all $d=0,1, \ldots n$and $n= p^a$, where $a$ is a positive integer. In this paper, we present some$q$-analogues of these congruences in the cases $m=2, 4$ for any positiveinteger $n$.

Some $q$-congruences involving central $q$-binomial coefficients