摘要
研究了三元变系数混合型欧拉函数方程φ（abc）=2φ（a）φ（b）＋6φ（c）的可解性问题,其中φ（n）为欧拉函数.利用初等数论相关内容及计算方法,给出了方程所有共计95组正整数解.所提出的求解技巧可用以求解其他相似类型的混合型欧拉函数方程.
We discussed the positive integer solutions of ternary variable coefficient hybrid Euler function equationφ（abc）=2φ（a）φ（b）＋6φ（c）, where φ（n） is Euler function. By using the related content of the elementary number theory and calculation method, a new mathematical technique for solving the equation is proposed, and a total of 95 positive integer solutions are obtained. The solution of the equation can be used to solve the similar Euler function equation problem.
作者
袁合才
王波
王晓峰
YUAN He-cai;WANG Bo;WANG Xiao-feng(School of Mathematics and Statistics,North China University of Water Resource and Electric Power Zhengzhou 450046,China;Office of Admission and Employment,Sanmenxia Polytechnic College,Sanmenxia 472000,China;School of Mathematical Sciences,Henan Institute of Science and Technology,Xinxiang 453003,China)
出处
《数学的实践与认识》
北大核心
2018年第12期303-307,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(U1304106)
河南省科技攻关项目(172102210367)
关键词
欧拉函数
混合型
丢番图方程
正整数解
Euler function
hybrid
diophantine equation
positive integer solutions
