Diophantine equation; prime; integer solution; Legendre symbol; congruence.
丢番图方程；素数；整数解；勒让德符号；同余。
Diophantine equation; Positive integer solution; congruence; Recurrent sequence.
丢番图方程；正整数解；同余；递归序列。
An elementary proof of the Diophantine equation (the equation abbreviated) is given by...
运用递推序列法，给出丢番图方程(方程序略)的一个初等解法。
On the diophantine equation is the number one branch, it has a long history and rich content.
不定方程是数论的一个分支，它有着悠久的历史与丰富的内容。
The method does not need solve the Diophantine equation, but reduces the computation of the algorithm.
这种方法无需求解丢番图方程，减少了控制算法的计算量。
Three century Diophantine one of the outstanding contribution that Greece algebra simplify, simplify algebraic created.
三世纪的丢番图的杰出贡献之一，就是把希腊代数学简化，开创了简化代数。
An elementary proof of the Diophantine equation (the equation abbreviated) is given by using recursion sequence method.
运用递推序列法，给出组合数丢番图方程(方程序略)的一个初等解法。
Chapter five presents the modified ABS algorithms for solving linear overdetermined linear Diophantine equations and inequations.
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 four gives ABS algorithms for solving linear Diophantine inequations and their application in integer linear programming.
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。
The advantages of the method are that it does not need solving the equation of Diophantine, and reduces the complexity of the algorithm.
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。
In this paper we study systems of Diophantine inequalities and equations with prime Numbers. We improve previous results by more delicate estimates of exponential sums.
本文研究了和素数有关的方程组和不等式组。通过更细致的指数和估计，我们改进了以前的结果。
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。
Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.
丢番图方程是数论中一个十分重要的研究课题，与代数数论、组合数学、代数几何等有密切联系。
By elementary rank transformations of matrix, a method has been obtained to solve linear diophantine equation with some variables. The method overcomes the deficiency of traditional method.
利用矩阵的初等列变换，给出了求解多元线性不定方程的一种方法，该方法改进了传统方法计算量大、步骤多的缺点。
Using the theorem of linear Diophantine equations and the Chinese remainder theorem, we have constructed a class of trap-door knapsack public-key cryptosystems, which have a better security.
利用不定方程理论及中国剩余定理，我们设计了一类陷门背包公开钥密码系统，它们具有更好的安全性。
In chapter three, the DLU and IILX algorithms for linear Diophantine equations are given based on the ABS algorithms. Corresponding properties, complexity and their application are discussed.
第三章在ABS算法的基础上给出了求解线性丢番图方程组的整隐式LU算法和整隐式LX算法，讨论了相应的ABS性质，并讨论了复杂性分析及其应用。
In chapter three, the DLU and IILX algorithms for linear Diophantine equations are given based on the ABS algorithms. Corresponding properties, complexity and their application are discussed.
第三章在ABS算法的基础上给出了求解线性丢番图方程组的整隐式LU算法和整隐式LX算法，讨论了相应的ABS性质，并讨论了复杂性分析及其应用。
应用推荐