首都师范大学学报（自然科学版）2025，Vol.46Issue(3)：16-23,8.DOI:10.19789/j.1004-9398.2025.03.003
数论函数方程ϕ8(n)=n/d的可解性
Solvability of the number theoretic functional equation ϕ8(n)=n/d
摘要
Abstract
By using the exact formula for the generalized Euler function ϕ8(n),for one of the formulas,this paper studies the solvability for the equation ϕ8(n)=n/d,where n is a positive integer and d is a positive factor of n>8.Use elementary methods and techniques to obtain all its positive integer solutions(n,d),when α=0,the positive integer solution of the equation is(n,d)=(9,9)(11,11).When α=1 and α=2,the equation has no positive integer solution.关键词
计算公式/广义欧拉函数/可解性/正因子/正整数解Key words
computation formula/generalized Euler function/solvability/positive factor/positive integer solution分类
数学引用本文复制引用
牛家星,高丽..数论函数方程ϕ8(n)=n/d的可解性[J].首都师范大学学报（自然科学版）,2025,46(3):16-23,8.基金项目
国家自然科学基金项目(11471007) （11471007）
