可表为两个Perrin数之和的纯位数  

Repdigits as sums of two Perrin numbers

作　　者：杨晋翔 杨鹏[1] YANG Jinxiang;YANG Peng(School of Science,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]辽宁科技大学理学院,辽宁鞍山114051

出　　处：《辽宁科技大学学报》2024年第4期310-315,共6页Journal of University of Science and Technology Liaoning

基　　金：辽宁省科技厅自然科学项目(2022-MS-356)。

摘　　要：本文主要研究Perrin序列的任意两项之和中的纯位数。此问题可以转化为丢番图方程求解,将方程转化为特殊形式,利用Baker方法给出解的一个上界,再通过缩减法将此上界缩减到可计算的范围内,利用Mathematica求出此范围内所有可表为两个Perrin数之和的两位数以上的纯位数分别为22、44与666。The repdigits that are sums of two Perrin numbers were studied mainly.The problem is equivalent to solving a Diophantine equation.First,the Baker method was applied to obtain an upper bound of this Diophantine equation.Then,this upper bound was reduced to a computable range by using the reduction method.Finally,with the help of Mathematica,all repdigits with more than two digits that can be expressed as the sum of two Perrin numbers within this range are found to be 22,44,and 666.

关 键 词：Perrin序列 纯位数 丢番图方程 对数线性型 Baker-Davenport引理 

分 类 号：O156.1[理学—数学]