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

### (10 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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