摘要
利用已有的广义欧拉函数的准确计算公式来研究方程φe(n)的可解性,其中n为正整数,d为n的正因子.并利用初等的方法和技巧给出方程φe(n)=n/d(e=1,2,4)的全部正整数解(n,d).
In order to generalize Lehmer's congruences from modulo prime squares to modulo integer squares,Cai defined the generalized Euler function. The paper studies the solvability of the Diophantine equationφe(n) =nd(e = 1, 2, 4), where n is a positive integer and d is a positive factor of n. By the elementary methods and techniques, the solvability of the Diophantine equation φe(n) =ndrelated to the generalized the Euler function φe(n)(e = 1, 2, 4) is studied. And then all solutions for the Diophantine equation φe(n) =n/d(e = 1, 2, 4)are given.
出处
《纯粹数学与应用数学》
2016年第5期481-494,共14页
Pure and Applied Mathematics
基金
国家自然科学基金重大项目(11401408)
四川省教育厅重点项目(142A0034)
四川省科技厅计划项目(2016JY0134)
关键词
广义欧拉函数
丢番图方程
正整数解
generalized Euler function
Diophantine equation
positive integer solution elementary method
conjecture
