On the generalized Hurwitz equations and the Baragar-Umeda equations

Abstract

We consider the generalized Hurwitz equation $a_1x_1^2+ \cdots +a_nx_n^2 = dx_1 \cdots x_n-k$ and the Baragar-Umeda equation $ax^2+by^2+cz^2=dxyz+e$ for solvability in integers.