【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■的全部解为(n,P_n)∈{(7,169),(8,408),(9,985)},其中P_n是Pell数，■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).更多还原

【Abstract】 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 ■ are(n,P_n)∈{(7,169),(8,408),(9,985)}, where P_n is the Pell number and ■ 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).更多还原