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The Congruent Number Problem and Its Connection with Elliptic Curves

13 February 2024, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

Number theory, a mathematical domain, centers on integers and their patterns. It often requires advanced methods to solve even simple problems. The Congruent Number Problem, unsolved for centuries, exemplifies this challenge. This survey article highlights how studying congruent numbers motivates exploring elliptic curves and how insights from these curves advance solving the Congruent Number Problem. The elegant connections between these subjects are striking.

Keywords

Congruent Numbers
Elliptic Curves
Connections

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Version History

Feb 13, 2024 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2024-5xmgx
D O I: 10.33774/coe-2024-5xmgx [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) declare that they have sought and gained approval from the relevant ethics committee/IRB for this research and its publication.

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