Some q-supercongruences modulo the fourth power of a cyclotomic polynomial

With the help of creative microscoping method recently introduced by Guo and Zudilin Chinese remainder theorem for coprime polynomials, we establish a q -supercongruence with two parameters modulo [ n ] ? ( ) 3 . Here = 1 ? / is -th cyclotomic polynomial in In particular, confirm recent conjecture give complete -analogue Long's supercongruence. The latter also generalization obtained Schlosser.