FPM 2001, vol. 7, no. 1, pp. 267-270

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 267-270

On the diophantine equation $(x/y)$ ^u + (y/z)^v + (z/x)^w = 4t

M. Z. Garaev

Abstract

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It is proved that the equation
$\bigl(\frac{x}{y}\bigr)^u+
\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$
has no solutions in positive integers $x, y, z, t, u, v, w$.

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On the diophantine equation (x/y)u + (y/z)v + (z/x)w = 4t

On the diophantine equation $(x/y)$ ^u + (y/z)^v + (z/x)^w = 4t