丢番图方程；正整数解；同余；递归序列。
Diophantine equation; Positive integer solution; congruence; Recurrent sequence.
丢番图方程；素数；整数解；勒让德符号；同余。
Diophantine equation; prime; integer solution; Legendre symbol; congruence.
这种方法无需求解丢番图方程，减少了控制算法的计算量。
The method does not need solve the Diophantine equation, but reduces the computation of the algorithm.
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。
An elementary proof of the Diophantine equation (the equation abbreviated) is given by...
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.
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.
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。
An elementary proof of the Diophantine equation (the equation abbreviated) is given by using recursion sequence method.
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.
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。
Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.
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。
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.
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