A Study on Two Special Ternary Quadratic Diophantine Equations

摘要

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.