A Study on Two Special Ternary Quadratic Diophantine Equations
Shreemathi Adiga
Department of Mathematics, Government First Grade College, Koteshwara, Kundapura Taluk, Udupi-576222, Karnataka, India.
M. A. Gopalan *
Department of Mathematics, Shrimati Indira Gandhi College, Trichy- 620 002, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
Hyperbolic paraboloids represented by the ternary quadratic diophantine equations given by (k+1)2x2 - k2y2=2z and k2ay2 – (a -k +1)x2 = ((k2 – 1)a+k – 1)z , a>k-1>0 are respectively considered. Employing matrix method, generation formula for integer solutions to each of the above hyperbolic paraboloids is constructed in the present study.
Keywords: Ternary quadratic, non-homogeneous quadratic, generation of solutions, hyperbolic paraboloid