Goldbach猜想在N3[1^2，2^2，3^2，……]中的推广  

The Generalization of Goldbach Conjecture in N3[12,22,32,……]

作　　者：叶彦谦[1] 叶惟寅[2] 

机构地区：[1]南京大学数学系,江苏南京210000 [2]南京师范大学数学系,江苏南京210000

出　　处：《新疆大学学报（自然科学版）》2004年第2期124-128,共5页Journal of Xinjiang University(Natural Science Edition)

摘　　要：文[1]已将Goldbach猜想推广到N2[12,22,32,……]中去,本文除了仿[1]将此猜想推广到N3[12,22,32,……],此外,还引进与Goldbach猜想对偶的另一猜想,借以研究N3[12,22,32,…]中之偶数表示为不同奇数的线性组合问题,得到可以补救[1]中所用方法之缺陷的新的结果,并由此提出另外的有意义的猜想.In [1],the author has generalized Goldbach conjecture to N_2[1~2,2~2,3~2,……]. This paper generalizes the conjecture to N_3[1~2,2~2,3~2,……].by imitating [1], in addition, we introduce another conjecture dual to Goldbach conjecture, by which we also study the problem that the even integers in N_3[1~2,2~2,3~2,……] can be represented to the linear combination of different odd integers, and we obtain some new result which can make up for the defects of the method given in [1].Furthermore, we pose another important conjecture.

关 键 词：GOLDBACH猜想 N3[1^2 2^2 3^2 ……] 线性组合 对偶猜想 

分 类 号：O156[理学—数学]