关于三角行数和正方形数的注记及算法构造  

Note and Algorithm Construction of Triangular Row Number and Square Number

作　　者：赵美利[1] 唐静[1] ZHAO Mei-li;TANG Jing(Chuzhou City Vocational College,Chuzhou 239000,China)

机构地区：[1]滁州城市职业学院,安徽滁州239000

出　　处：《电脑知识与技术》2021年第29期171-173,177,共4页Computer Knowledge and Technology

基　　金：安徽省职成教一般项目:区域民俗旅游经济发展与高职教育良性互动的策略研究——基于“大江北”规划(Azcj104);安徽省职业与成人教育学会2019年度教育科研规划课题5G时代高职计算机应用混合式教学改革探究(课题编号:Azcj118);滁州城市职业学院人文科研重点项目:大数据专业学生数学建模素养的影响因素分析和研究(2020sk09);2018年度高等学校省级质量工程(2018mooc156)。

摘　　要：三角形数是否能化为正方形数是一个有趣的数学问题,没有形成一定的结论,该文结合数列性质和佩尔方程,讨论了三角形数转化成正方形数的必要条件,设此三角形数的第n行的正整数为a_(n),把a_(n)从小到大构成一数列{a_(n)},则数列{a_(n)}是无穷数列,{a_(n)}有递推公式a_(n+2)=6a_(n+1)-a_(n+2),a_(1)=1,a_(2)=8,其通项公式为a_(n)=1/4[(3+2√2)^(n)]-1/2;则三角形数可化为正方形数,为研究三角形数和正方形数提供一定的参考价值,并利用了Java语言的大整数特征结合Eclipse集成开发环境,验证了其结论的正确性。Triangle number whether can into the square number is an interesting mathematical problems,not form a certain conclu⁃sion,based on the sequence of the nature and pell equation,The necessary and sufficient conditions for the triangle number to be transformed into a square number are discussed,Let the positive integer of a_(n) the nrow of the triangle number be,the a_(n) from small to large,constitute a_(n)a series sequence is infinite,has a recurrence formula a_(n+2)=6a_(n+1)-a_(n)+2,a_(1)=1,a_(2)=8 The general for⁃mula isa_(n)=1/4[(3+2√2)^(n)+(3-2√2)^(n)]-1/2;The number of triangles can be changed into the number of squares,which pro⁃vides some reference value for the study of the number of triangles and the number of squares.The correctness of the conclusion is verified by using the feature of large integer of JAVA language and Eclipse integrated development environment.

关 键 词：三角形数 正方形数 佩尔方程 大整数 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]