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

We prove that if at least one of the prime divisors of an odd integer U ≥ 3 is equal to 3 mod 4, then the ideal class group of the imaginary quadratic field $Q(\sqrt {1–4U^n } )$ contains an element of order n.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2009-12, Vol.137 (12), p.4025-4028
Main Author: LOUBOUTIN, STÉPHANE R.
Format: Article
Language:English
Subjects:
Algebra
College mathematics
Division
Exact sciences and technology
General mathematics
General, history and biography
Integers
Mathematical theorems
Mathematics
Number theory
Numbers
Sciences and techniques of general use
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Summary:We prove that if at least one of the prime divisors of an odd integer U ≥ 3 is equal to 3 mod 4, then the ideal class group of the imaginary quadratic field $Q(\sqrt {1–4U^n } )$ contains an element of order n.
ISSN:0002-9939
1088-6826
DOI:10.1090/s0002-9939-09-10021-7