The MHS algebra and supercongruences
Julian Rosen
TL;DR
This paper introduces a new technique utilizing infinite series and harmonic number generalizations to find and prove supercongruences, supported by software implementation, advancing the computational approach in number theory.
Contribution
It presents a novel method for discovering and proving supercongruences through series representations and provides software tools for automation.
Findings
Derived numerous new supercongruences
Developed an algorithmic approach for supercongruence proofs
Provided software for automated supercongruence discovery
Abstract
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain generalizations of the harmonic numbers. We apply the technique to derive many new supercongruences. We also provide software for finding and proving supercongruences using our technique.
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Taxonomy
TopicsAdvanced Mathematical Identities · Algebraic structures and combinatorial models · Quantum Mechanics and Applications