Abstract—In recent years, the common solution of pell equations is a hot field in indefinite equations. For example, the equations 1) mentioned in the paper. However, due to the diverse forms of such equations, many scholars have done more studies on the smaller values of k and m, and the main conclusions are focused on the estimation of solutions under some special forms of D1 and the specific values of D. So there is a lot of room for studying these kinds of equations. In this paper, we studied the common solution of the system of indefinite equations 2) mentioned in this paper by using the elementary method and the recursive property of solution sequence. If D is the case in this paper, the common solution of the equations is given.

Index Terms—The system of indefinite equations, pell equation, integer solution, common solution, odd prime.

Ran Yinxia is with Longnan Teachers College, College of Mathematics and Information Science, Longnan, China (email: ranyinxia@163.com).

Cite: Ran Yinxia, "Commom Solutions for a Class of Simultaneous Pell Equations," International Journal of Applied Physics and Mathematics vol. 9, no. 4, pp. 182-188, 2019.