In this paper, we search out the greatest common divisor of a group of integers and its combination by matrix elementary operation.
本文给出利用矩阵初等变换求一组整数的最大公因数,以及把它表示成这组数的组合的一个方法,此法常比一般“初等数论”教材中所给方法简单。
This paper first gets definition and theorems of integers matrices,and then to discusses a new method to find the greatest common factor of integers and solves linear indeterminate equation.
首先给出了整数矩阵的定义及性质,然后讨论了它在求整数的最大公因数和解整系数不定方程中的应用。
By using the method of number theory method of the greatest common factor of Fn and Fn+k are given,when n be POsitive,k=9,10.
利用数论方法，进一步探讨了Ｆｎ与Ｆｎ＋ｋ的最大公因数，其中ｎ是正整数，ｋ＝９，１０。
A new method of calculating the greatest common divisor;
最大公因数的一种新求法
It is proved that the elementary transformation of matrix can be used to obtain the greatest common factor of several integers and the greatest common divisor of multinomial.
证明了可以用矩阵的初等变换来求若干个正整数的最大公因数和若干个多项式的最大公因式,并通过具体实例来验证该方法。
The article proves that linear \$a 11 x 1+…+a 1n x n,…,a k1 x 1+…+a kn x n\$ of \$k·n(1≤k≤n)\$ unknowns and integer coefficient is sufficient and necessary condition of orthogonal system of pattern \$m\$, and the greatest common factor of all the factors of \$k\$ level of integer matrix \$(a\-\{ij\})\-\{ k×n\}\$ and \$m\$ is one.
文章证明了k个n( 1≤k≤n)元整系数线性型a1 1 x1 +… +a1nxn,… ,ak1 x1 +… +aknxn是模m的正交组的充要条件是整数矩阵 (aij) k×n 的所有k级子式与m的最大公因数为 1。
With the help of constructing matrix and applying elementary transfor-mation, this paper gives the simple and useful solution of the following three prob-lems in elementary number theory:greatest common factor and its times sum, in-definite equation, linear congruence expression series.
本文借助构造矩阵和施行初等变换,为初等数论中以下三个问题提供了简便实用的解法:最大公因数及其倍数和、不定方程,一次同余式组。