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