多元一次不定方程的整数解

多元1次不定方程的整数解

摘要

关键词：2元1次不定方程；多元1次不定方程；整除；最大公因数；整数解．

The Integer Solutions of

Multivariate Indeteminate Equation of the First Degree

ABSTRACT

This paper mainly studies multivariate indeteminate equation of the first degree have necessary and sufficent condition of integer solutions and extraction of integer solutions as well as the condition of the non-negative integer roots. Regarding this I carry on further study, when discussed about the integer solutions of duality indeteminable equation of the first degree, it has the condition of the negative integer roots. Therefore, I get the following conclusion: Supposes a, b both are the positive integers, c is a negative integer, and (a , b) =1, then in terms of c＜－(ab－a－b), duality indeteminable equation of the first degree ax+by=c

(1) has the negative integer roots, and the number of negative integer roots is equal to －[c／(ab)]－1 or －[c／(ab)].When c≥ab－a－b, duality indeteminable equation of the first degree

(1) has not the negative integer roots.

Key words: Duality indeteminable equation of the first degree; Multivariate indeteminate equation of the first degree; Divisible; Greatest common divisor; Integer solution.