Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8
type: Item
instance of: scholarly article
title: Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8
zbMATH Open document ID: 0877.11014
author: Boris Iskra
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-07-07T00:00:00Z
review text: The author proves that if \(p_1, \ldots, p_\ell\) are distinct primes satisfying \(p_i \equiv 3 \pmod 8\) and \((p_j/p_i) =-1\), \(j<i\), then the product \(p_1\ldots p_\ell\) is not a congruent number. A consequence of this result is the existence of an infinite sequence of distinct primes congruent to 3 modulo 8 such that any product of these primes is a non-congruent number.
reviewed by: Dimitros Poulakis
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 993539
zbMATH Keywords: elliptic curves
zbMATH Keywords: non-congruent numbers
zbMATH Keywords: product of primes
MaRDI profile type: Publication
full work available at URL: pjaa.72.168
OpenAlex ID: W2072954447
cites work: On the rank of an elliptic curve in elementary 2-extensions
cites work: Q3973403
DOI: 10.3792/PJAA.72.168
description: scientific article; zbMATH DE number 993539