Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial

Victor J. W. Guo, Michael J. Schlosser

Published 2021-01-24Version 1

Two $q$-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two $q$-supercongruences that were earlier conjectured by the same authors and involve $q$-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved $q$-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.