Some congruences with q-binomial coefficients and q-harmonic numbers

Abstract

In this paper, considering q-analogues and q-combinatorial identities, we gave some congruences including q-binomial coefficients and q- harmonic numbers. For example, for any prime number p and alpha is an element of Z(+), Sigma(p-1)(k=1) (-1)(k) q(-alpha pk)+( (k+1)()+ k)(2) [k] q [ alpha p - 1 k](q) = q(1- alpha p) /(1 - q(2))(2) ( q(alpha p+2) (q(p) - 2) + q(alpha p) - q(p) + q(2) ) [ p - 1] (q) (mod [p](q) (3)).