Ji-Cai Liu, Xue-Ting Jiang
Abstract
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We prove the divisibility conjecture on sums of even powers of $q$-binomial coefficients, which was recently proposed by Guo, Schlosser and Zudilin. Our proof relies on two $q$-harmonic series congruences due to Shi and Pan.
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We prove the divisibility conjecture on sums of even powers of $q$-binomial coefficients, which was recently proposed by Guo, Schlosser and Zudilin. Our proof relies on two $q$-harmonic series congruences due to Shi and Pan.
Key concepts: Divisibility rule, Binomial coefficient, Mathematics, Conjecture, Congruence relation, Central binomial coefficient, Gaussian binomial coefficient, Binomial (polynomial)