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.

中文翻译：

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一些 q-超同余模一个分圆多项式的平方和立方

通过对基本超几何级数采用特定恒等式，建立了包含两个自由参数的截断基本超几何级数的两个q-超同余。结果部分扩展了同一作者早先猜想的两个q-超同余，并涉及q-超同余模一个分圆多项式的平方和立方。一个新证明的q - 超同余甚至被推测为以分圆多项式的四次方为模。