Research Article

A remark on prime (non)congruent numbers

Published in: Quaestiones Mathematicae
Volume 45 , issue 12 , 2022 , pages: 1841–1853

DOI: 10.2989/16073606.2021.1977410

Author(s): Tim Evink Institute of Algebra and Number Theory, Ulm University, Germany , Jaap Top Bernoulli Institute, University of Groningen, The Netherlands , Jakob Dirk Top Bernoulli Institute, University of Groningen, The Netherlands

Keywords: 11G05 , 11A41 , 11R11 , 11N32 , Congruent number , elliptic curve , Selmer group , Shafarevich-Tate group , Bouniakowsky’s conjecture

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Abstract

This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form p = 8k +1, receives attention.

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