On Binary Quadratic Diophantine Equation 11x^2-10y^2=11

Abstract

This paper deals with the problem of obtaining non-zero distinct integer solutions to the non- homogeneous binary quadratic equation represented by the Pell-like equation . Different sets of integer solutions are presented. Employing the solutions of the above equation, integer solutions for other choices of hyperbolas, parabolas and straight lines are obtained. A special Pythagorean triangle is also determined. The formation of Diophantine 3 – tuples with suitable property is illustrated.