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

3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015

数学;化学;物理学

Urrutia, J.D.^1 ; Arañas, J.M.E.^1 ; Lara, J.A.C.L.^1 ; Maceda, D.L.P.^1

Polytechnic University of the Philippines, Philippines^1

关键词: Continued fraction;    Convergent;    Diophantine equation;    Pell equation;    Positive integers;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/622/1/012005/pdf
DOI  :  10.1088/1742-6596/622/1/012005

来源: IOP

【 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.