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

[摘要] 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.

[发布机构] Polytechnic University of the Philippines, Philippines^1

[效力级别] 化学

[关键词] Continued fraction;Convergent;Diophantine equation;Pell equation;Positive integers