TY  - JOUR
TI  - Some congruences with $q$−binomial sums
AB  - In this paper, using some combinatorial identities and congruences involving q− harmonic numbers, we establish congruences that for any odd prime p and any positive integer α , $sum_{k=1 (mod 2))}^{p-1} (-1)^{nk}tfrac{q^{-alpha npk+nbinom{k+1}{2}+2k }}{[k]_{q}}begin{bmatrix} alpha p-1 k end{bmatrix}_{q}^{n} quad (mod [p]_{q}^{2})$  $sum_{k=1 (mod 2))}^{p-1} (-1)^{nk}tfrac{q^{-alpha npk+nbinom{k+1}{2}+k }}{[k]_{q}}begin{bmatrix} alpha p-1 k end{bmatrix}_{q}^{n} tilde{H}_{k}(q) quad (mod [p]_{q}^{2})$ where n is any integer.
AU  - ömür, neşe
AU  - Gür, Zehra Betül
AU  - koparal, sibel
AU  - Elkhırı, laıd
DO  - 10.55730/1300-0098.3478
PY  - 2023
JO  - Turkish Journal of Mathematics
VL  - 47
IS  - 7
SN  - 1300-0098
SP  - 2006
EP  - 2027
DB  - TRDizin
UR  - http://search/yayin/detay/1208685
ER  -