On the generalized Hurwitz equations and the Baragar-Umeda equations

Abstract

We consider the generalized Hurwitz equation $a_1{x}_1^2+\cdots +a_n{x}_n^2=d{x}_1\cdots x_n-k$ and the Baragar-Umeda equation $a{x}^2+b{y}^2+c{z}^2=dxyz+e$ for solvability in integers.

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