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May 2004 On the solution of $x^2 + dy^2 = m$
Julius Magalona Basilla
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 40-41 (May 2004). DOI: 10.3792/pjaa.80.40

Abstract

A simple proof of the validity of Cornacchia's algorithm for solving the diophantine equation $x^2 + dy^2 = m$ is presented. Furthermore, the special case $d=1$ is solved completely.

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Julius Magalona Basilla. "On the solution of $x^2 + dy^2 = m$." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 40 - 41, May 2004. https://doi.org/10.3792/pjaa.80.40

Information

Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1106.11042
MathSciNet: MR2062797
Digital Object Identifier: 10.3792/pjaa.80.40

Subjects:
Primary: 11Y16
Secondary: 11D09

Keywords: Cornacchia's algorithm , Diophantine equations , Quadratic forms

Rights: Copyright © 2004 The Japan Academy

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Vol.80 • No. 5 • May 2004
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