Complete solutions of the simultaneous Pell equations x(2)-24y(2)=1 and y(2) - pz(2)=1

作者：Ai, Xiaochuan; Chen, Jianhua; Zhang, Silan^*; Hu, Hao

来源：Journal of Number Theory, 2015, 147: 103-108.

DOI：10.1016/j.jnt.2014.07.009

• Diophantine equations
• Pell equation
• Simultaneous Pell equations

We prove that the simultaneous Pell equations
{x(2) - 24y(2) =1 , y(2) - pz(2) = 1
where p is a prime, have positive integer solutions only in the cases of p = 11 and p = 2. Furthermore, the only solutions are (x, y, z, p) = (49, 10, 3, 11) and (x, y, z, p) = (485, 99, 70, 2).

• 出版日期2015-2
• 单位武汉大学; 中国人民解放军海军工程大学; 华中农业大学