Solvability of some entangled Diophantine equations
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1369-1374
https://doi.org/10.4134/BKMS.2014.51.5.1369
Printed September 30, 2014
Poo-Sung Park
Kyungnam University
Abstract : 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
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