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On a class of insoluble binary quadratic diophantine equations

Published online by Cambridge University Press:  22 January 2016

Franz Halter-Koch
Franz Halter-Koch*
Affiliation:
Institut für Mathematik, Karl-Franzens-Universität Halbärthgasse 1/I A-8010 Graz, Österreich
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The binary quadratic diophantine equation

is of interest in the class number problem for real quadratic number fields and was studied in recent years by several authors (see [4], [5], [2] and the literature cited there).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 141 - 151
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[ 1 ] Dirichlet, P. G. L., Vorlesungen über Zahlentheorie, Braunschweig 1893, Chelsea Reprint 1968.Google Scholar
[ 2 ] Halter-Koch, F., Quadratische Ordnungen mit grofier Klassenzahl, J. Number Theory, 34 (1990), 82–94.Google Scholar
[ 3 ] Kaplan, P., Williams, K. S., The distance between ideals in the orders of a real quadratic field, L’Enseig. Math., 36 (1990), 321–358.Google Scholar
[ 4 ] Mollin, R. A., On the insolubility of a class of Diophantine equations and the non-triviality of the class numbers of related real quadratic fields of Richaud-Degert-type, Nagoya Math. J., 105 (1987), 39–47.CrossRefGoogle Scholar
[ 5 ] Yokoi, H., On the diophantine equation x2 = py2 == ±4q and the class number of real subfields of a cyclotomic field, Nagoya Math. J., 91 (1983), 151–161.CrossRefGoogle Scholar