SOLUTION OF BINARY QUADRATIC DIOPHANTINE EQUATION: y2 = 32x2 +73

Abstract

In this paper, the binary quadratic equation y²=32x²+73, which represents a hyperbola, also known as positive form of Pell equation is analyzed for finding its non-zero distinct integer solutions. Knowing an integral solution of the given hyperbola, integer solutions for other choices of hyperbolas and parabolas are presented. A few relations between the solutions are presented, using the solutions; a special Pythagorean triangle is constructed.