A necessary condition for p and 2p to be congruent for a prime p ≡ 1 (mod 8)

被引：1

作者：

Das, Shamik ^{[1
]}

Saikia, Anupam ^{[2
]}

机构：

[1] HBNI, Harish Chandra Res Inst, Dept Math, Chhatnag Rd, Jhunsi 211019, India

[2] Indian Inst Technol, Dept Math, Gauhati 781039, Assam, India

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2023年 / 227卷 / 07期

关键词：

Congruent number; Elliptic curve; Class number; CLASS NUMBER;

D O I：

10.1016/j.jpaa.2023.107335

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider primes p = 1 (mod 8). We show that p = 1 (mod 16) if 2p is a congruent number. We further show that the class number of Q(root 2p) must be divisible by 4 if p is a congruent number.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：12

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