On the Quadratic Diophantine Equation (x1x2 ) + x1 x2 = 8

Abstract

In this paper, authors have studied the quadratic Diophantine equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8; ð‘¥1,ð‘¥2 ∈ ð‘−{0}, where ð‘−{0} represents the set of non zero integers, for determining the ordered pairs (ð‘¥1,ð‘¥2) ∈ ð‘−{0} × ð‘−{0} that satisfy the equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8. It was shown by the results that the ordered pairs (ð‘¥1,ð‘¥2) = (4,1),(−4,−1) ∈ ð‘−{0} × ð‘−{0} are the only solutions of the quadratic Diophantine equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8.