On the Diophantine Equations of the Form \( x^2 - kxy + ky^2 + 2ny = 0 \)

In this article, we determine all values of \( k \) for which the equation \( x^2 - kxy + ky^2 + 2ny = 0 \), where \( n = 3,4,5,6,7 \), has infinitely many positive solutions.

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Publication Details

Journal
European Journal of Pure and Applied Mathematics
Published
2025-05-01
DOI
https://doi.org/10.29020/nybg.ejpam.v18i2.6004
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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0.00
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article

On the Diophantine Equations of the Form \( x^2 - kxy + ky^2 + 2ny = 0 \)

Nattaporn Thongngam, Supawadee Prugsapitak
European Journal of Pure and Applied Mathematics
Advanced Mathematical Theories and Applications
article

On the Diophantine Equations of the Form \( x^2 - kxy + ky^2 + 2ny = 0 \)

Nattaporn Thongngam, Supawadee Prugsapitak
article en

Abstract

In this article, we determine all values of \( k \) for which the equation \( x^2 - kxy + ky^2 + 2ny = 0 \), where \( n = 3,4,5,6,7 \), has infinitely many positive solutions.

European Journal of Pure and Applied MathematicsVol. 18(2)
Prince of Songkla University (TH)
Openalex Percentile: Top 93%
Advanced Mathematical Theories and Applications
DOIOpen Access PDFOpenAlex
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On the Diophantine Equations of the Form \( x^2 - kxy + ky^2 + 2ny = 0 \) — Nattaporn Thongngam, Supawadee Prugsapitak · European Journal of Pure and Applied Mathematics (2025) | TGRS Research Map | TGRS