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

Nguyen Xuan Tho

doi:10.4171/em/543

JournalsemVol. 80, No. 4pp. 170–174

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

Nguyen Xuan Tho
Hanoi University of Science and Technology, Vietnam

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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 $m$ .

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Nguyen Xuan Tho, On the equation $x / y + y / z + z / x = 4^{m}$ . Elem. Math. 80 (2025), no. 4, pp. 170–174

DOI 10.4171/EM/543