丢番图方程

Diophantine equation is an important branch of the number theory, and also the most active in the field of mathematics though the whole history.

不定方程又称为丢番图方程，是数论的重要分支学科，是历史上最活跃的数学领域之一。

An elementary proof of the Diophantine equation is given by using recursion sequence method.

摘要运用递推序列法，给出组合数丢番图方程的一个初等解法。

Diophantine equation is an old problem, especially, its more difficult to apply primary method to resolve the problems related to Diophantine equation.

不定方程是一个古老的丢番图问题，特别是应用初等方法去解决不定方程的有关问题更是不宜；许多解法很简单也易看懂，但却不宜想到。

Diophantine equation is an old problem, especially; it's more difficult to apply primary method to resolve the problems related to Diophantine equation. There are many solutions, which are very simple and also easy to understand, but hard to think out.

不定方程是一个古老的丢番图问题，特别是应用初等方法去解决不定方程的有关问题更是不易；许多解法很简单也易看懂，但却不易想到。

There are many solutions, which are very simple and also easy to understand, but hard to think out. Another name of indeterminate equation is Diophantine equation, its an important branch of the number theory, and also the most active in the field of mathematics through the whole history.

不定方程又称为丢番图方程，是数论的重要分支学科，是历史上最活跃的数学领域之一。1980年，著名的数学家柯召和孙琦在我国出版了第一部专门研究不定方程的专著《谈谈不定方程》。

Fermat and led them to numerous general results which Diophantus himself only hinted. Perhaps more important, however, is the fact that this work, as a work of algebra, was in effect a treatise on the analysis of problems.

史学界一直认为丢番图仅满足于得到不定方程的一个解，本文的中心论点之一是揭示丢番图解法的一般性，亦即丢番图知道解的多样性，只要取不同的值，便可利用他的方法得到其它解。

In this paper,we use the results of Ljunggren,Cohn,Bennett and Walsh, Chen to give the bound and effective algorithm of positive integer solution number of two Diophantine equations.

本文利用Ljunggren，Cohn，Bennett和Walsh以及陈建华等人的结果，给出了两个丢番图方程正整数解的解数上界和有效算法。

Linear Diophantine equations appear often in modeling and practical application, which play an important part in transportation.

线性丢番图方程组的求解是实际应用中经常遇到的一类问题，在物流、运输中起着重要的作用，从而对线性丢番图方程解的探讨变得尤为必要。

The security of these new cryptosystems depends on some NP-complete problems in the theory of Diophantine equations and on the difficulty of large number decomposition.

这些体制的安全性依赖于求解丢番图方程中的一些NP完全问题和大数的素因子分解的困难性。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷