摘要
该文研究丢番图方程ay(y+1)(y+2)(y+3)=bx(x+1)(x+2)(x+3),其中a,b是互素的正整数.利用高次丢番图方程的结果证明了:当(a,b)=(8,9)时,该方程仅有一组正整数解(x,y)=(32,33);当(a,b)=(m^(2),4p^(2k))时,该方程没有正整数解,其中m,k是任意正整数,p是素数且gcd(m,2p)=1.
This paper studies the Diophantine equation ay(y+1)(y+2)(y+3)=bx(x+1)(x+2)(x+3),where a,b are coprime positive integers.It is proved by results about Diophantine equations of higher order that,this equation has only one positive integer solution when(a,b)=(8,9)and has no positive integer solution when(a,b)=(m^(2),4p^(2k)),where m and k are arbitrary positive integers,p is a prime and gcd(m,2p)=1.
作者
何宗友
HE Zong-you(Shenzhen Jingtian Precision Technology Co.,Ltd.,Shenzhen 518118,China)
出处
《南宁师范大学学报（自然科学版）》
2023年第3期15-18,共4页
Journal of Nanning Normal University：Natural Science Edition
关键词
丢番图方程
PELL方程
高次丢番图方程
正整数解
Diophantine equation
Pell equation
Diophantine equation of higher order
positive integer solution
作者简介
何宗友(1972-),男,陕西西乡人,主要研究数论.Email:hezongyou126.com。
