A Preliminary Report on Search for Good Examples of Hall's Conjecture
St{\aa}l Aanderaa, Lars Kristiansen, Hans Kristian Ruud
TL;DR
This paper introduces a new algorithm designed to find good examples of Hall's Conjecture, successfully discovering five new instances in initial searches, advancing the understanding of this mathematical problem.
Contribution
The paper presents a novel algorithm capable of detecting all good examples of Hall's Conjecture within a specified search space, marking progress in the search for solutions.
Findings
Discovered five new good examples of Hall's Conjecture
Developed and implemented a comprehensive search algorithm
Demonstrated the algorithm's effectiveness in initial experiments
Abstract
This paper is a preliminary report on our search for new good examples of Hall's Conjecture. We present a new algorithm that will detect all good examples within a given search space. We have implemented the algorithm, and our executions have so far found five new good examples.
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Taxonomy
TopicsAdvanced Mathematical Theories · Analytic Number Theory Research · Mathematics and Applications