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

JOURNAL OF NUMBER THEORY

卷:176

Article

Aoki, Miho¹  Kishi, Yasuhiro² 

[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

关键词: Quadratic fields;    Quartic fields;    Class numbers;   

DOI  :  10.1016/j.jnt.2016.12.007

来源: Elsevier

【 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.

【 授权许可】

Free