可表为3个纯位数串联的Pell数  

Pell numbers which are concatenations of three repdigits

作　　者：周建华 瞿云云 朱山山 曾吉文[2] ZHOU Jianhua;QU Yunyun;ZHU Shanshan;ZENG Jiwen(School of Mathematical Sciences,Guizhou Normal University,Guian New District 550025,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵安新区550025 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2023年第3期481-486,共6页Journal of Xiamen University：Natural Science

基　　金：贵州省科学技术基金(黔科合基础-ZK[2021]一般313号);贵州师范大学学术新苗基金(黔师新苗[2021]B10号)。

摘　　要：利用代数数对数的线性形式和Baker-Davenport约减方法,找到了丢番图方程P_(n)=a…a m_(1)次b…b m_(2)次c…c m_(3)次的全部解为(n,P_(n))∈{(7,169),(8,408),(9,985)},其中P_(n)是Pell数,a…a m_(1)次b…b m_(2)次c…c m_(3)次是以10为基的3个纯位数的串联,且a,b,c∈{0,1,…,9},a>0,a≠b,b≠c,m i∈Z+(i=1,2,3).In this paper,by using linear forms in logarithms of algebraic numbers and Baker-Davenport reduction method,we find that all solutions of the Diophantine equation P_(n)=a…a m_(1)times b…b m_(2)times c…c m_(3)times are(n,P_(n))∈{(7,169),(8,408),(9,985)},where P_(n)is the Pell number and a…a m_(1)times b…b m_(2)times c…c m_(3)times is the concatenation of three repdigits in base 10 with a,b,c∈{0,1,…,9},a>0,a≠b,b≠c and m i∈Z+(i=1,2,3).

关 键 词：Pell数 纯位数串联 对数线性形式 Baker-Davenport约减方法 

分 类 号：O156[理学—数学]