Some congruences with q - binomial sums

Abstract

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 alpha,Sigma(p-1)(k=1 (mod 2)) (-1)(nk) q(-alpha npk+n(k+1 2)+2k)/[k](q) [alpha p - 1 k](q)(n) (mod [p](q)(2)),andSigma(p-1)(k=1 (mod 2)) (-1)(nk) q(-alpha npk+n(k+1 2)+2) [alpha p - 1 k](q)(n) (H) over tilde (k)(q) (mod [p](q)(2)),where n is any integer.