2个推广的Smarandache方程及其正整数解  

On Two Generalizations of Smarandache Equation and Their Positive Integer Solutions

作　　者：黄炜[1] 

机构地区：[1]宝鸡职业技术学院基础部,陕西宝鸡721013

出　　处：《西南师范大学学报（自然科学版）》2013年第2期12-14,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11071194);陕西省教育厅自然科学基金(09JK432)

摘　　要：采用初等方法与解析方法,对2个含有n个变量的推广的Smarandache方程(x1a1/x1+1/x1ax1)+(x2a1/x2+1/x2ax2)+…+(xna1/xn+1/xnaxn)=2na(x1a1/x1+1/x1ax1)·(x2a1/x2+1/x2ax2)·…·(xna1/xn+1/xnaxn)=(2a)n进行了研究,并得出其有正整数解x1=x2=x3=…=xn=1.Utilizing the elementary methods and analytic methods, two generalizations of Smarandache Equation have been studied, and completely solved on the positive integer solution of the two generaliza- tions of Smarandache Equation （x1a^1/x1＋1/x1a^x1）＋（x2a^1/x2＋1/x2a^x2）＋…＋（xna1/x^n＋1/xna^xn）=2na（x1a^1/x1＋1/x1a^x1）·（x2a^1/x2＋1/x2a^x2）·…·（xna^1/xn＋1/xna^xn）=（2a）^n There exists positive integer solution if and only if x1 =x2 =x3 xn =1.

关 键 词：Smarandache方程 可解性 正整数解 

分 类 号：O156.2[理学—数学]