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

Abstract

In this paper, authors have studied the quadratic Diophantine equation (𝑥1 𝑥2 ) +𝑥1𝑥2 = 8; 𝑥1,𝑥2 ∈ 𝑍−{0}, where 𝑍−{0} represents the set of non zero integers, for determining the ordered pairs (𝑥1,𝑥2) ∈ 𝑍−{0} × 𝑍−{0} that satisfy the equation (𝑥1 𝑥2 ) +𝑥1𝑥2 = 8. It was shown by the results that the ordered pairs (𝑥1,𝑥2) = (4,1),(−4,−1) ∈ 𝑍−{0} × 𝑍−{0} are the only solutions of the quadratic Diophantine equation (𝑥1 𝑥2 ) +𝑥1𝑥2 = 8.