Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the solution of $x^2-dy^2=\pm m$

Julius M. Basilla and Hideo Wada

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Abstract

An improvement of the Gauss' algorithm for solving the diophantine equation $x^2-dy^2=\pm m$ is presented. As an application, multiple continued fraction method is proposed.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 8 (2005), 137-140.

Dates
First available in Project Euclid: 1 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1130858932

Digital Object Identifier
doi:10.3792/pjaa.81.137

Mathematical Reviews number (MathSciNet)
MR2177847

Zentralblatt MATH identifier
1152.11320

Subjects
Primary: 11D09: Quadratic and bilinear equations 11Y05: Factorization 11Y16: Algorithms; complexity [See also 68Q25]

Keywords
Quadratic form diophantine equation continued fraction method prime decomposition

Citation

Basilla, Julius M.; Wada, Hideo. On the solution of $x^2-dy^2=\pm m$. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 8, 137--140. doi:10.3792/pjaa.81.137. https://projecteuclid.org/euclid.pja/1130858932


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References

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