奶牛数之和为好奇数
Curious numbers as sum of two Narayana's cows numbers
王佳文 1杨鹏 1刘佳奇 1任政1
作者信息
- 1. 辽宁科技大学 理学院,辽宁 鞍山 114051
- 折叠
摘要
本文旨在找到所有可以表示为两个奶牛数之和的好奇数.奶牛数列满足三阶递归关系:Nn=Nn-1 +Nn-3(n≥3)及N0=0、N1=N2=1.针对奶牛数之和为好奇数的问题,建立相应丢番图方程,将方程整理成不同形式,通过对数线性型求出各个未知量的一个较大的上界;再通过缩减方法,把各个未知量的较大上界缩减为一个可计算上界;最后,根据未知量的可计算上界,应用Mathematica得出所有可表示为两个奶牛数之和的好奇数.
Abstract
This paper aims to identify all curious numbers that can be represented as the sum of two Narayana's cows numbers.Narayana's cows sequence satisfies the third-order linear recurrence relation Nn=Nn-1 +Nn-3,n≥3 and n0=0,N1=N2=1.For the problem of the sum of Narayana's cows numbers being a curious num-bers,a corresponding Diophantine equation is established.Different forms of the equation are arranged,and a larger upper bound for each unknown variable is obtained through linear forms in logarithms.Then,using the reduction method,the upper bound of each unknown variable is reduced to a computable upper bound.Final-ly,based on the computable upper bound of the unknown variables,Mathematica is used to find all curious numbers expressible as the sum of two Narayana's cows numbers.
关键词
奶牛序列/纯位数/好奇数/对数线性型/缩减方法Key words
Narayana's cows sequence/repdigits/curious numbers/linear forms in logarithms/reduction method引用本文复制引用
基金项目
辽宁省自然科学基金(2022-MS-356)
出版年
2024
NETL
NSTL
万方数据