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 Solvability of some entangled Diophantine equations Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1369-1374 https://doi.org/10.4134/BKMS.2014.51.5.1369Printed 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 Downloads: Full-text PDF