关于不定方程 x(x+1)(x+2)(x+3)= 66y(y+1)(y+2)(y+3)  

On the Diophantine equation x(x+1)(x+2)(x+3)=66y(y+1)(y+2)(y+3)

作　　者：林丽娟 LIN Lijuan(Department of General Studies,Chongqing Chemical Industry Vocational College,Chongqing 401228,China)

机构地区：[1]重庆化工职业学院通识教育学院,重庆401228

出　　处：《贵州师范大学学报（自然科学版）》2021年第3期76-79,118,共5页Journal of Guizhou Normal University：Natural Sciences

基　　金：重庆化工职业学院校级科研课题(HZY2020-KJ06)。

摘　　要：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证明了在(M,N)=(1,66)时不定方程Mx(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3)仅有8组非平凡整数解(x,y)=(8,2),(54,18),(8,-5),(54,-21),(-11,2),(-11,-5),(-57,18),(-57,-21)。Based on the basic solution of Pell equation,recursive sequence,congruence theory and other elementary methods,we have proved that the Diophantine equation Mx(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3)with(M,N)=(1,66)has nontrivial integer solution,(x,y)=(8,2),(54,18),(8,-5),(54,-21),(-11,2),(-11,-5),(-57,18),(-57,-21)。

关 键 词：不定方程 PELL方程 递推序列 整数解 

分 类 号：O156.2[理学—数学]