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1)  Sequence of granularly resolvent clauses
粒归结序列
2)  Special sequence of granularly resolvent clauses
特殊粒归结序列
3)  recursive sequence
递归序列
1.
The relation between the iteration of projective function and the linear recursive sequences of order 2 is given.
先给出射影函数的迭代与 2阶线性递归序列的关系 ,进而得到此递归序列与Bernoulli数的一个恒等
4)  recurrent sequence
递归序列
1.
This paper proves that the Diophantine equation has only integer solution with the help of the Pell method taking an integer>1 as module to make inconsistency,the natures of recurrent sequences and equivalent Pell equation.
采用对方程取某个正整数M>1为模来制造矛盾的同余法和利用递归序列的性质,以及Pell方程的性质,证明不定方程x3-1=13y2仅有整数解(x,y)=(1,0)。
2.
In this paper,the author has proved, with two method of contradictor recurrent sequences and congruence when modules of some positive integer M>1, that the Diophantine equation x~3+1=19y~2 has only integer solution(x,y)=(1,0).
利用两种初等的方法,即对方程取某个正整数M>1为模来制造矛盾的同余法和递归序列法,证明了不定方程x3 -1=19y2 仅有整数解(x,y)=(1,0),从而进一步的证明了方程x2 -19y2 =-13无整数解;方程x2 -3r2 =-3仅有整数解(1。
3.
With the method of recurrent sequence and congruences,proved that the Diophantine equation x3+1 =37y2has only integer solution(x,y)=(-1,0),(11,±6).
利用递归序列,同余式证明了丢番图方程x 3+1=37y2,仅有整数解(x,y)=(-1,0),(11,±6)。
5)  recurrence sequences
递归序列
1.
Formulas for simple and direct computations for Euler--Bernoulli polynomials of n variablesare presented,some identities containing recurrence sequences and Euler--Bernooulli polynomials of n variables have been established.
给出简捷计算n元Euler-Bernoulli多项式的公式,建立一些包含递归序列和上述多项式的恒等式。
6)  recurrence sequence
递归序列
1.
In this paper using the method of recurrence sequences we show that there does not exist positive solution in the equation of the title.
证明过程中仅涉及到了初等的数论知识,就是采用了递归序列的方法,证明了不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)无正整数解,同时这个证明过程也给出了这个不定方程组的全部整数解,它们是(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3)。
2.
In this paper the author gives a general expression and the property of a 3degreelinear recurrence sequence by using Jordan s normal form of the coefficient matrix.
用3阶线性递归序列的系数矩阵的若当标准形,给出了3阶线性递归序列的通项及一个性质。
3.
Some identities involving recurrence sequences and higher order multivariable Nrlund Euler_Bernoulli polynomials are established.
 给出了高阶多元N rlundEuler多项式和高阶多元N rlundBernoulli多项式的定义,讨论了它们的一些重要性质,建立了一些包含递归序列和上述多项式的恒等式·
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