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A problem of Ozanam

Part of: Diophantine equations Arithmetic algebraic geometry

Published online by Cambridge University Press:  02 February 2009

Andrew Bremner
Andrew Bremner
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA (bremner@asu.edu)
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Abstract

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A problem posed in the early eighteenth century asks for right-angled triangles, each of whose sides exceeds double the area by a perfect square. We summarize known results and find such triangles with the smallest possible standard generators.

Keywords

Pythagorean triangleareasquareelliptic curve

MSC classification

Secondary: 11D25: Cubic and quartic equations 11G05: Elliptic curves over global fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 37 - 44
Copyright
Copyright © Edinburgh Mathematical Society 2009