An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five

被引：2

作者：

Aoki, Miho ^{[1
]}

Kishi, Yasuhiro ^{[2
]}

机构：

[1] Shimane Univ, Interdisciplinary Fac Sci & Engn, Dept Math, Matsue, Shimane 6908504, Japan

[2] Aichi Univ Educ, Fac Educ, Dept Math, Kariya, Aichi 4488542, Japan

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 176卷

关键词：

Quadratic fields; Quartic fields; Class numbers;

D O I：

10.1016/j.jnt.2016.12.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a new infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five. Let n be a positive integer that satisfy n 3 (mod 500) and n not equivalent to 0 (mod 3). We prove that 5 divides the class numbers of both Q(root 2 - F-n) and Q(root 5(2 - F-n)) where Fn, is the nth Fibonacci number. (C) 2017 Elsevier Inc. All rights reserved.

引用

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页码：333 / 343

页数：11

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