基本解释：递归数论
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In this paper,the author has proved that the Diophantine equation x3+64=21y2 has only an integer solution(x,y)=(-4,0),(5,±3) and then gives all integer solution of x3+64=21y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residue.利用递归数列、同余式和平方剩余几种初等方法,证明了不定方程x3+64=21y2仅有整数解(x,y)=(-4,0),(5,±3);给出了x3+64=21y2的全部整数解。
In this paper,the author has proved that the Diophantine equation x3+27=7y2 has only an integer solution(x,y)=(-3,0),(1,±2) and then gives all integer solution of x3+27=7y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residu利用递归数列、同余式和平方剩余几种初等方法,证明了不定方程x3+27=7y2仅有整数解(x,y)=(-3,0),(1,±2);给出了x3+27=7y2的全部整数解。
By applying the properties of determinant, the general formula of a usual type of linear recursive sequence is studied.应用行列式的有关性质，研究了一般形式的线性递归数列的通项公式。
In this paper,the authors use recurrent sequence to prove that the diophantine equation x3-1=26y2 has only integer solutions(x,y)=(1,0),(3,±1),(313,±1086).用递归数列方法证明了方程x3-1=26y2全部整数解是(1,0),(3,±1),(313,±1086)。
By using congruence and recurrent sequence,the author has proved that the Diophantine equation x3+1=86y2 has only the integer solution(x,y)=(-1,0),(7,±2).利用递归数列、同余式证明了丢番图方程x3+1=86y2仅有整数解(x,y)=(-1,0),(7,±2)。
By using the method of recurrent sequence,the Diophantine equation x3-8=13y2 has been proven to have the only integer solution(x,y)=(5,±3) with gcd(x,y)=1.利用同余式和递归数列的方法,证明了不定方程x3-8=13y2仅有适合(x,y)=1的整数解(x,y)=(5,±3)。
The Recursive Equation of Homogeneous Linear Recurrent Sequence of Number Formed by General Term Formula;由通项公式构造齐次线性递归数列的递归方程
Method for matrix solution of constant coefficient recursive sequences general term equation;常系数递归数列通项公式的矩阵求法
A Tentative Study of Constant Coefficients Homogeneous Linear Recurrent Number Sequence;常系数齐次线性递归数列的初步探讨
The General Formula of A Usual Type of Linear Recursive Sequence;一般形式的线性递归数列的通项公式
Computation Invariable Coefficient the Number of Times is Different Linear Recursion Sequence Special Solution Simple Method;常系数非齐次线性递归数列求特解的简易方法
Prove and Application of Sequences General Term Equation;一类线性递归数列通项公式的证明和应用
Methods for obtaining the general term formulae of a kind of non-linear、non-homogeneous recursive sequences;一类非线性、非齐次递归数列的通项公式的求法
The Methods of Mathematical Thought in Finding the General Term of First Order Constant Coefficient Linear Recursive Sequence;求一阶常系数线性递归数列通项公式的数学思想方法
Research on the Problems of Form Numbers in Two Recurrent Sequences Arising in the Units of Quadratic Field Q(3～(1/3));二次域Q（3～（1/3））的单位给出的两个递归数列中的形数问题研究
Change of Variables for General Formula of Non-homogeneous Linear Recursive Sequence with Constant Coefficients;常系数非齐次线性递归数列通项公式计算的通项变换法
Recursive TimeOuts is the total number of recursive query sending timeouts.递归超时是指递归查询发送超时总数。
Recursive Query Failure is the total number of recursive query failures.递归查询失败是指归查询失败的总数。
Linear Recurring Sequence over the Matrix and Its Cryptography Properties;矩阵上的线性递归序列及密码学特性
The Resolution of Magic Square by Means of Full Permutation and Recursion--C++ Programe Design;用全排列和递归求解“魔方”——C++程序设计
Recursive TimeOut/sec is the average number of recursive query sending timeouts in each second.递归超时/秒是指每秒递归查询发送超时的平均数。
The Recursive and Non-recursive Backtrack Algorithms for Nine Different Numerals Constitute an Equation of Multiplication九位不同数字乘法等式的递归与非递归回溯算法
Recursive Query Failure/sec is the average number of recursive query failures in each second.递归查询失败/秒是指归查询失败的平均数。
Strong Consistency of Regression Function Recursive Kernel Estimator under Negatively Associated Samples;NA样本回归函数递归型估计的强相合性
