摘要
利用初等数学方法和欧拉函数积性等相关性质,在z为素数的条件下,讨论了三变元欧拉函数方程φ(xyz)=φ(x)(φ(y)+φ(z))的可解性问题,并求出当x≤100时方程的所有正整数解,其中φ(n)是欧拉函数,n为正整数。文章所采用的求解方法具有一定的普遍适用性,可用于求解类似的欧拉函数方程。
By adopting the elementary mathematical method and related properties of Euler function,with as the prime number,solvability of Euler function equation with three variables is studied.When,the positive integer solution of the equation is obtained,in which is the Euler function and is the positive integer.The proposed calculation method has certain universality,thus can be used to solve other similar Euler function equations.
作者
席小忠
孙乐
冷春勇
XI Xiaozhong;SUN Le;LENG Chunyong(Institute of Mathematics and Computer Science,Yichun College,Yichun 336000,Jiangxi,China)
出处
《江西理工大学学报》
CAS
2020年第5期96-100,共5页
Journal of Jiangxi University of Science and Technology
基金
国家自然科学基金资助项目(11861069)
宜春学院“六卓越一拔尖”教学质量工程项目——数学与应用数学卓越教师培养计划。
关键词
欧拉函数
不定方程
正整数解
最大公因数
Euler function
indefinite equation
positive integer solution
GCD
