Bulletin of the
Korean Mathematical Society BKMS

We show that the Diophantine equation \[ a\,Q(x_1,x_2) + b\,Q(x_3,x_4) + c\,Q(x_5,x_6) = abc \] has integral solutions for arbitrary positive integers $a, b, c$ when $Q(x,y)$ is a norm form for some imaginary quadratic fields.

Keywords: Diophantine equations, quadratic forms, Hermitian lattices

MSC numbers: Primary 11D09; Secondary 11E39