NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

We prove that the class number of the imaginary quadratic field $\Q(\sqrt{2^{2k}-3^n})$ is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

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Bibliographic Details
Published inGlasgow mathematical journal Vol. 51; no. 1; pp. 187 - 191
Main Author KISHI, YASUHIRO
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2009
Subjects
11R11
11R29
Mathematics
Quadratic programming
11R29
11R11
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Summary:We prove that the class number of the imaginary quadratic field $\Q(\sqrt{2^{2k}-3^n})$ is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.
Bibliography:istex:6E6043C268C0F121217A21F28D881C38E63C086C
ark:/67375/6GQ-M1PHW5Q1-C
ArticleID:00462
PII:S001708950800462X
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ObjectType-Article-2
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ISSN:0017-0895
1469-509X
DOI:10.1017/S001708950800462X