Victor J. W. Guo and Michael J. Schlosser

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

(9 pages)

Abstract. 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.

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