S(S≥2)元一次不定方程的整数解

THE INTEGER SOLUTION TO THE LINEAR INDEFINITE EQUATION IN S VARIABLES (S≥2)

设S≥2,S元一次不定方程是指a_1x_1十a_2x_2十…十a_sx_s=n其中a_i(i=1,2,…,s)与n都是给定的整数,a_1a_2…a_s≠0.本又通过S元a_1,a_2,…,a_5的辗转相除法,给出上式的整数解的结构公式.

Supposing there is S≥2 , the linear indefinite equation in S variables refers to the following form: a1x1 + a2x2 +…+ ascs = n , in which ai (i = 1,2, …, s ) and n are given integral numbers, a1 a2… as ≠0. This paper provides a structural formula of integer solution for the above form by means of division algorithm of S variables a1,a2,… , as.