Congruences with q-harmonic numbers and q-binomial coefficients

Laid Elkhiri (), Sibel Koparal () and Neşe Ömür ()
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Laid Elkhiri: University of Tiaret, USTHB Bab Ezzouar
Sibel Koparal: University of Bursa Uludağ
Neşe Ömür: University of Kocaeli

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 639-648

Abstract: Abstract In this paper, we show the congruences $$\sum \limits _{k=m}^{p-1}q^{k}{k \brack m}_{q}\widetilde{H}_{k,2}(q)$$ ∑ k = m p - 1 q k k m q H ~ k , 2 ( q ) $$\pmod {\left[ p\right] _{q}^{2}}$$ ( mod p q 2 ) and $$\sum \limits _{k=m}^{p-1}q^{k}{k \brack m}_{q}\widetilde{H}_{k}^{2}(q)$$ ∑ k = m p - 1 q k k m q H ~ k 2 ( q ) $$\pmod {\left[ p\right] _{q}^{2}}$$ ( mod p q 2 ) with a prime number $$p>2$$ p > 2 and $$m=0, 1, 2,.., p-1$$ m = 0 , 1 , 2 , . . , p - 1 .

Keywords: Congruence; q-Analog; q-Harmonic number; 11A07; 11B65 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00401-6

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