# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Real quadratic fields with class numbers divisible by $n$. (English) Zbl 0287.12007

From the introduction: The goal of this note is to prove the following theorem:

Theorem 1: For all positive integers $n$, there are infinitely many real quadratic fields $ℚ\left(\sqrt{{\Delta }\left(x\right)}\right)$ with class numbers divisible by $n$, where ${\Delta }\left(x\right)={x}^{2n}+4$.

The corresponding theorem for complex quadratic fields was originally proved by T. Nagell [Abh. Math. Sem. Univ. Hamb. 1, 140–150 (1922; JFM 48.0170.03)].

##### MSC:
 11R11 Quadratic extensions 11R29 Class numbers, class groups, discriminants
##### Keywords:
real quadratic fields; divisibility of class number