摘要
主要运用pell方程、递推序列、同余式及(非)平方剩余等一些初等方法,证明了不定方程6x(x+1)(x+2)(x+3)=7y(y+1)(y+2)(y+3)仅有正整数解(x,y)=(25,24).沿用该文相同思路和方法得出关于不定方程mx(x+1)(x+2)(x+3)=ny(y+1)(y+2)(y+3)其中(m,n)=(6,11)和(m,n)=(5,11)时均无正整数解.
Such elementary methods as Pell equation,recursive sequence,congruence and quadratic(non-)residue are mainly used to prove that the diophantine equation 6 x(x+1)(x+2)(x+3)=7 y(y+1)(y+2)(y+3)has only the positive integer solution(x,y)=(25,24).Based on similar ideas and methods,this paper proves that the diophantine equation mx(x+1)(x+2)(x+3)=ny(y+1)(y+2)(y+3)has no positive integer solution when(m,n)=(6,11)or(m,n)=(5,11).
出处
《西南师范大学学报(自然科学版)》
CAS
北大核心
2017年第10期17-21,共5页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
不定方程
整数解
递归数列
diophantine equation
interger solution
recurrence sequence