不定方程x^3+1=333y^2的整数解  

The Integral Solutions of Diophantine Equation x^3 + 1 = 333y^2

作　　者：邱克娥[1] 雍进军[1] 陶磊[1] 肖钦欢 QIU Ke-e;YONG Jin-jun;TAO Lei;XIAO Qin-huan(Guizhou Education University,Guiyang,Guizhou,550018,China)

机构地区：[1]贵州师范学院,贵州贵阳550018

出　　处：《凯里学院学报》2018年第6期22-24,共3页Journal of Kaili University

基　　金：贵州省教育厅青年科技人才成长项目(黔教合KY字(2017)205);贵州师范学院学生校级自然科学基金项目(2018DXS097)

摘　　要：利用同余式及Pell方程解的性质证明不定方程x^3+1=333y^2仅有整数解(x,y)=(-1,0),(11,±2).The integral solutions of diophantine equation x^3+1=333y^2 is discussed by congruence sequence and some properties of the solutions to Pell equation.It is proved that the diophantine equation x^3+1=333y^2 only has integer solutions(x,y)=(-1,0),(19,±14).

关 键 词：不定方程 整数解 同余式 

分 类 号：O156[理学—数学]