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The q-binomial coefficients are the polynomial cousins of the traditionalbinomial coefficients, and a number of identities for binomial coefficients canbe translated into this polynomial setting. For instance, the familiarvanishing of the alternating sum across row n of Pascal's triangle is capturedby the so-called Gaussian Formula. In this paper, we find a q-binomialcongruence which synthesizes this result and Fleck's congruence for binomialcoefficients.

A generalization of the Gaussian formula and a q-analog of Fleck's congruence