On the Diophantine equations x 2 ? 27y 2 = 1 and y 2 ? 2 p z 2 = 25

2018 2nd International Workshop on Renewable Energy and Development

能源学;经济学

Zhao, Jianhong^1

Department of Teachers and Education, Lijiang Teachers College, Lijiang, Yunnan

674199, China^1

关键词: Diophantine equation;    Integer solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/153/4/042001/pdf
DOI  :  10.1088/1755-1315/153/4/042001

来源: IOP

【 摘 要 】

In recent years, scholars have paid much attention to the problem of solving the diophantine equations x 2 - D 1 y 2 = m, (D 1 ∈ Z +, m ∈ Z) and y 2 - D 2 z 2 = n, (D 2 ∈ Z +, n ∈ Z). At present, there are only a few conclusions on x 2 - D 1 y 2 = land y 2 - D 2 z 2 = 1, and the conclusions mainly concentrated in the number of solutions and the range of it, see Ref [1] and [3]. For odd numbers D 2, the integer solution of x 2 - D 1 y 2 = land y 2 - D 2 z 2 = 4, see Ref [4] - [6]. For even numbers D 2, the integer solution of (2), see Ref [7] - [11]. Up to now, there is no relevant result on the integer solution of x 2 - 27y 2 = 1 and y 2 - 2p z 2 = 49, this paper mainly discusses the integer solution of it.