1) 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)。
2) 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 Nrlund 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·
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) 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。
5) rational recurrence sequence
有理递归序列
1.
Global asymptotic stability of a class of rational recurrence sequence;
一类有理递归序列的全局渐近稳定性(英文)
6) polynomial recursion sequenee
多项式递归序列
1.
A polynomial recursion sequenee is constructed to obtain a calculational method of ni=1 m which takes the calculation of ni=1i m as its special conditio
构造一个多项式递归序列 ,得到 ni =1[a +(i -1)d] m 的一种求法 ,使 ni=1im 的计算成特殊情
补充资料：递归序列
递归序列
recursive sequence
递归序列【re皿叙s闪.叮犯e或rec~nt sequence;的3-BPaT“叨noc月e压oBaTe几I.H0cT‘」 一个序列“。，“，，…，满足关系式 a。+，+自“。+p一!+”’+cl，“，一0，其中cl，…，c，是一些常数·如果己知前p项，则根据上述关系式可以依次算出其余各项.递归序列的一成嘴睽蜘好是Fi加nacci)抑Ul，l，2，3，5，8，一(a。*:=。，.*，+a。，。、，=。、=1).一个递归级数是一个幂级数(Power series)。。+“;x+“Zx’+…，其系数构成递归序列.这种级数表示处处有定义的有理函数. BC3一3【补注1从多方面研究递归序列的一篇很好的参考文献是〔Al].
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