五次完全幂的少位数三进制展开  

Perfect Powers of Five with Few Ternary Digits

作　　者：罗家贵 李想 LUO Jiagui;LI Xiang(School of Mathematics and Information,China West Normal University,Nanchong 637009,Sichuan,China;Primary School Affiliated to China West Normal University,Meishan 620575,Sichuan,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学附属小学,四川眉山620575

出　　处：《数学年刊（A辑）》2021年第4期359-378,共20页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11871058);四川省教育厅重大专项(No.16ZA0173)。

摘　　要：本文讨论了Michael Bennett在[Bennett M,Bugeaud Y,Mignotte M.Perfect powers with few binary digits and related Diophantine problem[J].Ann Sc Norm Super Pisa Cl Sci,2013,XII:941–953.]中提出的一类丢番图方程,即五次完全幂的少位数三进制展开.作者证明了丢番图方程3^(a)+3^(b)+2=n^(5),a>b>0有唯一的正整数解(a,b,n)=(3,1,2).In this paper,the authors analyze a diophantine equation raised by Michael Bennett in[Bennett,M.,Bugeaud,Y.,and Mignotte,M.,Perfect powers with few binary digits and related Diophantine problem,Ann.Sc.Norm.Super.Pisa Cl.Sci,2013,vol.XII,pp.941–953.]that is pivotal in establishing that powers of five has few digits in its ternary expansion.They show that(a,b,n)=(3,1,2)is the only positive integer solution of Diophantine equation 3^(a)+3^(b)+2=n^(5)with a>b>0.

关 键 词：丢番图方程 三进制 同余 正整数解 

分 类 号：O156.7[理学—数学]