On the Diophantine equations x2 ? 7y2 = 1 y2 ? Dz2 = 9

3rd International Conference on Energy Equipment Science and Engineering

Zhao, Jianhong^1 ; Yang, Lixing^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/10.1088/1755-1315/128/1/012126/pdf
DOI  :  10.1088/1755-1315/128/1/012126

来源: IOP

【 摘 要 】

The integer solution of diophantine equations x2- D1y2= m, (D1∈ Z+, m ∈ Z) and y2- D2z2= n, (D2∈ Z+, n ∈ Z) is a matter of great concern. Researchers study for different m, n and D1, D2, and obtain some correlation results as follows. When m = 1, n = 1, the diophantine equations turns into x2- D1y2= 1 and D2z2= 1. At present, there are only a few conclusions on it, see Ref [1] and [2]. When m = 1, n = 4, the diophantine equations turns into x2- D1y2= 1 and D2z2= 4. For even numbers D1, D2, the integer solution see Ref [3] - [9]. When m = 1, n = 16, the diophantine equations turns into x2- D1y2= 1 and D2z2= 16. The previous conclusions see Ref [10]. When m = 1, n = 9, the diophantine equations turns into x2- D1y2= 1 and D2z2= 9. Up to now, there is no relevant result on the integer solution of (5), this paper mainly discusses the integer solution of (5) when D1= 7, D2is an even number.