Some congruences from the Karlsson-Minton summation formula
Junhang Li, Yezhenyang Tang, Chen Wang
TL;DR
This paper uses the Karlsson-Minton summation formula to prove new supercongruences related to a known supercongruence, confirming recent conjectures in number theory.
Contribution
It introduces novel supercongruences derived from the Karlsson-Minton formula, extending previous results and confirming recent conjectures.
Findings
Proved two new supercongruences for odd primes.
Confirmed conjectures of V.J.W. Guo.
Extended the application of Karlsson-Minton summation formula.
Abstract
Let be an odd prime. In this paper, by using the well-known Karlsson-Minton summation formula, we mainly prove two supercongruences as variants of a supercongruence of Deines-Fuselier-Long-Swisher-Tu, which confirm some recent conjectures of V.J.W. Guo.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Algebra and Geometry