关于不定方程x(x+1)(x+2)(x+3)=70y(y+1)(y+2)(y+3)  

On the Diophantine Equation x(x+1)(x+2)(x+3)=70y(y+1)(y+2)(y+3)

作　　者：林丽娟 罗明 LIN Li-juan;LUO Ming(Department of General Studies,Chongqing Chemical Industry Vocational College,Chongqing 401147,China;School of Mathematics Science,Chongqing Normal University,Chongqing 400047,China)

机构地区：[1]重庆化工职业学院通识教育学院,重庆401147 [2]重庆师范大学数学科学学院,重庆400047

出　　处：《数学的实践与认识》2020年第15期307-313,共7页Mathematics in Practice and Theory

摘　　要：当N为给定正整数时,不定方程x(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3)的求解是数论中未彻底解决的问题.利用Pell方程基本解性质、递推序列、同余思想以及二次剩余等初等方法得到并证明了在N=70时该不定方程仅有正整数解(x,y)=(5,1).As N are both give positive integer,the Diophantine Equation,x(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3),is not got completely solved in number theory.Based on the basic solution of Pell Equation,Recursive Sequence and Congruence Theory and other elementary methods,N=70 has been proved.Moreover,the Diophantine Equation has positive integer solution(x,y)=(5,1).

关 键 词：不定方程 PELL方程 递推序列 同余 正整数解 

分 类 号：O156[理学—数学]