文章基本信息

标题：On the Diophantine equations x 2 − 27y 2 = 1 and y 2 − 2 p z 2 = 25
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作者：Jianhong Zhao
期刊名称：IOP Conference Series: Earth and Environmental Science
印刷版ISSN：1755-1307
电子版ISSN：1755-1315
出版年度：2018
卷号：153
期号：4
页码：042001
DOI：10.1088/1755-1315/153/4/042001
语种：English
出版社：IOP Publishing
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 − 2^p z ² = 49, this paper mainly discusses the integer solution of it.