不定方程ax^3+by^3+cz^3=0解的一个判定定理及其解法探究

A decision theorem and solution on indefinite equation such as ax^3+by^3+cz^3=0

形如axn+byn+czn=0类不定方程解的判定,求解算法,及其解数的研究一直是国内外探讨的1个热门问题,迄今为止,还没有1个完美的结果.本文应用模分解理论,对于指数n=3给出了1个关于方程有解的1个判定定理,并对方程的解法进行了探讨.随着密码学与编码学的兴起和发展,数论的应用越来越广泛,因此研究此问题对推动数论的发展及其在密码及编码上的应用,都有一定的理论意义.

The discriminance, the solving arithmetic, and the solution numbers of indefinite equation such as ax^3＋by^3＋cz^3=0 is a popular issue at home and abroad. Up to now,It has not a perfect result. For the index n = 3 ,this paper applies mold theory to give a decision theorem to discriminate whether the equation has solution and discuss the method of its solution . With the rise and development of modern Cryptography and Coding Theory , the application of Number Theory becomes more and more extensive. It can impulse the application in modern Cryptography and Coding Theory. So that the study on the problem has important theory meaning to develop Number Theory.