Implication of Continued Fraction and Metallic Ratios to Resolve Binary Quadratic Diophantine Equations

V. Pandichelvi; S. Saranya

doi:https://doi.org/10.14445/22315373/IJMTT-V68I12P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 12 | Year 2022 | Article Id. IJMTT-V68I12P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I12P503

Implication of Continued Fraction and Metallic Ratios to Resolve Binary Quadratic Diophantine Equations

V. Pandichelvi, S. Saranya

Received	Revised	Accepted	Published
19 Oct 2022	20 Nov 2022	03 Dec 2022	15 Dec 2022

Citation :

V. Pandichelvi, S. Saranya, "Implication of Continued Fraction and Metallic Ratios to Resolve Binary Quadratic Diophantine Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 12, pp. 13-15, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I12P503

Abstract

In this manuscript, the set of non-zero integer solutions (x,y) to some Diophantine equations of the forms x2-rxy-y2=±1 where 4≤ r≤ 9 by relating continued fraction and metallic ratios are investigated. Furthermore, the collection of all such pair (x,y) are confirmed by MATLAB programs.

Keywords

Diophantine equation, Metallic ratio, Continuous Fraction.

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