几个不定方程在Q((-11)^(1/2))和Q((-43)^(1/2))中的解　　　  

On Solutions of Several Diophantine Equations in Q((-11)^(1/2)) and Q((-43)^(1/2))

作　　者：王永亮[1] 

机构地区：[1]菏泽学院数学系,山东菏泽274015

出　　处：《温州大学学报（自然科学版）》2008年第2期20-23,共4页Journal of Wenzhou University(Natural Science Edition)

摘　　要：根据代数数论的理论,将初等数论中的一些结论推广到更大的代数整数环中,应用这些结论确定了几个著名的不定方程在虚二次域的整数环中的解,指出了费尔玛方程在比整数环更大的环中也没有非平凡解.In this paper, some conclusions in elementary number theory are generalized to rings of algebraic integers. Then with the help of these results, all solutions of several Diophantine equations in the rings of integers of two quadratic imaginary fields are determined, which implies that the Fermat equation has no non-trivial solutions in these rings.

关 键 词：虚二次域 整数环 不定方程 

分 类 号：O156.2[理学—数学]