On the equation $x/y+y/z+z/x=4^{m}$

We provide an elementary proof that the equation in the title has no solutions in the positive integers. This extends recent work of the author [Elem. Math. 78 (2023), 168–170] from m=1 to arbitrary positive integers m .

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Publication Details

Journal
Elemente der Mathematik
Published
2025-01-29
DOI
https://doi.org/10.4171/em/543
Primary Topic
Differential Equations and Numerical Methods
Type
article
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article

On the equation $x/y+y/z+z/x=4^{m}$

Nguyen Xuan Tho
Elemente der Mathematik
Differential Equations and Numerical Methods
article

On the equation $x/y+y/z+z/x=4^{m}$

Nguyen Xuan Tho
article en

Abstract

We provide an elementary proof that the equation in the title has no solutions in the positive integers. This extends recent work of the author [Elem. Math. 78 (2023), 168–170] from m=1 to arbitrary positive integers m .

Elemente der MathematikVol. 80(4)
Hanoi University of Science and Technology (VN)
Openalex Percentile: Top 97%
Differential Equations and Numerical Methods
DOIOpen Access PDFOpenAlex
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On the equation $x/y+y/z+z/x=4^{m}$ — Nguyen Xuan Tho · Elemente der Mathematik (2025) | TGRS Research Map | TGRS