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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Class numbers of quadratic fields determined by solvability of Diophantine equations
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by R. A. Mollin PDF
Math. Comp. 48 (1987), 233-242 Request permission

Abstract:

In the literature there has been considerable attention given to the exploration of relationships between certain diophantine equations and class numbers of quadratic fields. In this paper we provide criteria for the insolvability of certain diophantine equations. This result is then used to determine when related real quadratic fields have class number bigger than 1. Moreover, based on criteria which we find for the solvability of a certain class of diophantine equations, we are able to determine when the class number of related imaginary quadratic fields is divisible by a given integer.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 233-242
  • MSC: Primary 11R11; Secondary 11R29
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0866112-5
  • MathSciNet review: 866112