丢番图

在本文中，我们讨论了欧几里得和丢番图著作中与数论有关的某些问题。

In this article , we discuss some questions with respect to number theory in the works of Euclid and diophantus .

求解线性丢番图方程组及不等式组的ABS算法

ABS Algorithms for Solving Linear Diophantine Equations and Inequations

混合幂为2,3，a和b的丢番图不等式

Diophantine inequality with mixed powers 2,3 , a and b

第五章给出了求解超定线性丢番图方程组和不等式组的修正ABS算法。

Chapter five presents the modified ABS algorithms for solving linear overdetermined linear Diophantine equations and inequations .

丢番图逼近（DiophantineApproximation）理论的发展始于两个世纪前，是数论的一个重要分支。

The development of the theory of Diophantine approximation started two centuries ago .

第四章给出了求解线性丢番图不等式组的ABS算法及其在整线性规划中的应用。

Chapter four gives ABS algorithms for solving linear Diophantine inequations and their application in integer linear programming .

联立丢番图逼近中的一个分形集的Hausdorff维数

The Hausdorff dimension of a fractal set in simultaneous Diophantine approximation

与Abel差集有关的一个丢番图方程的解

The Solutions of the Diophantine Equation about Abel-Difference Sets

CME分析中的丢番图方程求解

Diophantine Equation Solution in CME Analysis

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。

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 .

本文利用推广的pell方程法给出了一类指数丢番图方程的全部正整数解。

This paper gives an the solutions in positive integer of some exponential Diophantine equations by applying generalized Pell 's equation method .

丢番图逼近、环面T~2上的Gevrey亚椭圆性与几乎周期运动

Diophantine Approximation , Gevrey Hypoellipticity and Almost Periodic Motion on the Torus T ~ 2

另一个主要方面是Skolem的p-adic方法，主要应用于攻克某些特定的丢番图方程。

Skolem 's p-adic method , which is used in attacking certain Diophantine equations , is another powerful application of p-adic numbers .

在20世纪早期，为了解决丢番图方程组或不等式组相关的问题，MacMahon提出分拆分析方法（即Omage算子）。

In the early 1900s , Major Percy A. MacMahon developed Partition Analysis ( i.e. , the Omega operator ) as a computational method for solving problems in connection with linear diophantine inequalities and equations .

基于Clarke（1987）等提出的广义预测控制，采用1步预报避步递推的方法，代替原文中递推求解丢番图方程进行大范围预测，在此基础上得到改进型的广义预测控制。

In this paper , A modified generalized prediction control ( MGPC ), based on GPC proposed by Clarke etc ( 1987 ), is developed . One multistep predictor in a successive one-step manner was proposed instead of the large range predictive using the recursive solution to the Diophantine equations .

一类有关虚二次域理想类群的指数丢番图方程

An Exponential Diophantine equation concerning ideal class groups of imaginary quadratic fields

多元样条、分片代数曲线及线性丢番图方程组

Multivariate Splines , Piecewise Algebraic Curves and Linear Diophantine Equations

整数环的某些扩环上的一些丢番图方程

Some Diophantine Equations on Certain Extention Rings of Integers

求解线性丢番图方程（组）的串、并行算法

Sequential and Parallel Algorithms for Solving Linear Diophantine Equations

混合幂丢番图不等式的一个注记

A Note on Diophantine Inequalities With Mixed Powers

用丢番图方程构作公开钥密码体制

On setting up public-key cryptosystems using Diophantine Equations

丢番图&背包型公开钥密码体制

Diophantine - knapsack type public - Key Cryptosystem

一个加性混合幂丢番图不等式（Ⅰ）

One Additive Diophantine Inequality with Mixed Powers (ⅰ)

关于单位分数的丢番图方程

On the Diophantine Equation of Unit Fraction

关于指数型丢番图方程的整数解

On Integer Solutions of Exponential Diophantine Equations

证明了该算法能够抵抗低密度攻击和联立丢番图逼近攻击等。

It is shown that the cryptosystem is secure against low-density attacks and the simultaneous Diophantine approximation attacks .

运用递推序列法，给出组合数丢番图方程（方程式略）的一个初等解法。

An elementary proof of the Diophantine equation ( The equation abbreviated ) is given by using recursion sequence method .

对2000年ACISP会议上的一个快速公钥密码算法进行了安全性分析，给出了该算法的安全性与联立丢番图逼近问题以及格上的最小向量问题之间的关系。

The relation of the security of the cryptosystem with the simultaneous Diophantine approximation problem and the shortest vector problem over lattices is clarified .

这种方法的优点在于无需求解丢番图方程，减少了控制算法的计算量。

The advantages of the method are that it does not need solving the equation of Diophantine , and reduces the complexity of the algorithm .

首先，在第2章介绍了广义预测控制的基本算法，其中所提的各种算法，均需在线求解丢番图方程和大矩阵求逆，运算量大，不利于实时控制。

All the algorithms of GPC in Chapter II have to solve Diophantine equation and the inversion of big matrix online . So real time control is infeasible .