In a recent article, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences. At the end, they propose some supercongruences as conjectures. Here we prove one of them, including a new companion enumerating Abelian squares, and we leave some remarks for the others.
Amdeberhan, T., Tauraso, R. (2017). Two triple binomial sum supercongruences. JOURNAL OF NUMBER THEORY, 175, 140-157 [10.1016/j.jnt.2016.11.014].
Two triple binomial sum supercongruences
Tauraso, Roberto
2017-01-01
Abstract
In a recent article, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences. At the end, they propose some supercongruences as conjectures. Here we prove one of them, including a new companion enumerating Abelian squares, and we leave some remarks for the others.File in questo prodotto:
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