关于一类Diophantus方程sum from i=1 to n (xi)=пmultiply from i=1 to n (xi)的整解  

On the Integral Solutions of a Class of Diophantine Equations sum from i=1 to n (xi)=пmultiply from i=1 to n (xi)

作　　者：黄崇智[1] 

机构地区：[1]内江师范学院数学系,四川内江641112

出　　处：《内江师范学院学报》2002年第4期14-19,共6页Journal of Neijiang Normal University

摘　　要：作者在本文中 ,引入了解型概念 ,并将解型分为平凡、正、负、0 -混合及非 0 -混合五种 ,从而极大地降低了问题的复杂性 ,得到了两个关键定理 (定理 4以及定理 1 0 )提供了求 Diophantus方程∑ni=1xi= ni=1xi 的全部正解型及全部非 0 -混合解型的途径。从而 ,解决了这两种解型的个数及构造问题。In this paper the writer has introduced the conception solution type and divided it into five kinds viz.the trivial, the positive,the negative,the 0 mixed and the non 0 mixed solution type,by means of which the complexity of the problem was enormously reduced.Two key theorems were obtained.With them the approaches to obtaining all the positive as well as all the non 0 mixed solution types of Diophantine equation ∑ni=1x i=ni=1x i were suggested,so that the problems of the number and structure of these two solution types were completely solved.

关 键 词：Diophautus方程 整解 平凡解型 正解型 负解型 非0-混合解型 

分 类 号：O156[理学—数学]