On the Diophantine Equation Ax2 — KXY + Y2 + Lx = 0

Abstract

For any positive integer a ≥ 2, we have shown that there are infinitely many pairs of positive integer l and k so that the equation Ax2 — Kxy + y2 + Lx = 0 has infinitely many positive integer solutions. Moreover, we have shown the forms of k and l that may take. We also presented the tables of solution for 2 ≤ a ≤ 10, for some integers 1 ≤ n ≤ 5.