M. Z. Garaev, “On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$”, Fundam. Prikl. Mat., 2001, Volume 7, Issue 1,Pages <nobr>267

Short communications

On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$

M. Z. Garaev

M. V. Lomonosov Moscow State University

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

UDC: 511.3

Received: 01.11.1998