Abstract
In this paper, we show the congruences \(\sum \limits _{k=m}^{p-1}q^{k}{k \brack m}_{q}\widetilde{H}_{k,2}(q)\) \(\pmod {\left[ p\right] _{q}^{2}}\) and \(\sum \limits _{k=m}^{p-1}q^{k}{k \brack m}_{q}\widetilde{H}_{k}^{2}(q)\) \(\pmod {\left[ p\right] _{q}^{2}}\) with a prime number \(p>2\) and \(m=0, 1, 2,.., p-1\).
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Communicated by B. Sury.
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Elkhiri, L., Koparal, S. & Ömür, N. Congruences with q-harmonic numbers and q-binomial coefficients. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00401-6
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DOI: https://doi.org/10.1007/s13226-023-00401-6