摘要
不定方程是数论研究的一个重要分支,不仅其自身发展活跃,而且离散数学的各个领域也有重要的应用,对于解决现实问题有着重要的作用.主要利用pell方程、递归数列、同余式和平方剩余几种初等方法,针对D=73时,不定方程x^3±64=Dy^2的解进行讨论,证明了不定方程x^3±64=73y^2仅有整数解(x,y)=(+4,0).
The Diophantine equation is an important branch of number theory research, not only itself development is active but also it has important application in discrete mathematics, as a result, it plays an important role in solving real problems. Many scholars at home and abroad extensively and deeply study it for many years. By the elementary methods such as pell equation, recurrent sequence, congruence expression, and square residue, the solution to the Diophantine equation x^3±64 = Dy^2 is discussed when D= 73, and this paper proves that the Diophantine equation x^3±64 = 73y^2 only has integer solution （ x, y） = （ ＋^- 4,0）.
出处
《重庆工商大学学报（自然科学版）》
2016年第1期26-28,42,共4页
Journal of Chongqing Technology and Business University:Natural Science Edition
基金
国家自然科学基金(11471265)
关键词
不定方程
整数解
递归数列
同余式
Diophantine equation
integer solution
recurrent sequence
congruence expression
