JP Journal of Algebra, Number Theory and Applications
Volume 12, Issue 2, Pages 129 - 155
(December 2008)
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BINARY QUADRATIC FORMS, AMBIGUOUS IDEALS, MARKOV NUMBERS, AND SUMS OF SQUARES
R. A. Mollin (Canada)
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Abstract: We provide an overview of the rather formidable, but oft-not-cited connections among binary quadratic forms, continued fractions, and ambiguous ideals, with applications to Markov numbers and sums of squares problems. In particular, emphasis is placed on the role of the intimate links between ambiguous forms and ideals in determining some Markov conjecture problems as well as solving problems concerning sums of two squares when the underlying real quadratic field has a ring of integers with no unit of norm –1. |
Keywords and phrases: binary quadratic forms, Diophantine equations, sums of squares, quadratic fields, ambiguous ideals, continued fractions, Markov numbers. |
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