An algorithm for proving terminating hypergeometric identities, and thus binomial coefficients identities, is presented. It is based upon Gosper's algorithm for indefinite hypergeometric summation. A MAPLE program implementing this algorithm succeeded in proving almost all known identities. Hitherto the proof of such identities was an exclusively human endeavor.Â

q-Series: their development and applications in analysis, number theory, combinatorics, physics, and computer algebra, CBMS series 66 (Amer

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