Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the divisibility of the class number of imaginary quadratic fields

Katsumasa Ishii

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Abstract

Let $U$ be an integer with $U>1$. If $n$ is even with $n\geq 6$, then the class number of $\mathbf{Q}(\sqrt{1-4U^{n}})$ is divisible by $n$ except $(U,n)=(13,8)$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 8 (2011), 142-143.

Dates
First available in Project Euclid: 3 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1317647396

Digital Object Identifier
doi:10.3792/pjaa.87.142

Mathematical Reviews number (MathSciNet)
MR2843095

Zentralblatt MATH identifier
1262.11093

Subjects
Primary: 11R11: Quadratic extensions

Keywords
Imaginary quadratic field class number divisibility

Citation

Ishii, Katsumasa. On the divisibility of the class number of imaginary quadratic fields. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 8, 142--143. doi:10.3792/pjaa.87.142. https://projecteuclid.org/euclid.pja/1317647396


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