Some supercongruences arising from symbolic summation
Ji-Cai Liu
TL;DR
This paper extends two supercongruences related to hypergeometric series using combinatorial identities derived from symbolic summation, building on previous conjectures and recent confirmations.
Contribution
It introduces new supercongruences based on combinatorial identities from symbolic summation, expanding the understanding of hypergeometric series congruences.
Findings
Extended two supercongruences on hypergeometric series
Confirmed conjectures by Guo and Schlosser
Built upon recent proofs by Jana and Kalita
Abstract
Based on some combinatorial identities arising from symbolic summation, we extend two supercongruences on partial sums of hypergeometric series, which were originally conjectured by Guo and Schlosser and recently confirmed by Jana and Kalita.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics