关于不定方程x^3-8=3py^2  

On the Diophantine Equation x^3-8=3py^2

作　　者：余启港[1] 王顺金[1] 于新月[1] 张梅娜[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2011年第3期103-104,110,共3页Journal of South-Central University for Nationalities：Natural Science Edition

摘　　要：利用递归数列与Pell方程解的相关性质和结论,证明了不定方程x3-8=3py2(其中p=5,13,29,37,53,61)当x为奇数时无整数解.In this paper,we prove that the diophantine equation x3-8=3py2（for p=5,13,29,37,53,61）has not integer solution when x is an odd number,with the help of the congruence method and the properties of recurrent sequences and Pell equation.

关 键 词：不定方程 整数解 递归数列 

分 类 号：O156[理学—数学]