On a problem of F.Smarandache
For any positive integer n, the famous Euler function φ(n) is defined as the number of all integers m with 1≤m≤n such that (m, n) = 1. In his book Only problems, not solutions (see unsolved problem 52), Professor F.Smarandache asked us to find the smallest positive integer kk(n), such that φk(n) = 1, where φ1(n) = φ(n), φ2(n) = φ(φ1(n)),…, and φk(n) = φ(φk-1(n)). In this paper, we using the elementary method to study this problem, and prove that for any positive integer n, k(n) = minm : 2m≥n, m ∈N, where N denotes the set of all positive integers.
The Smarandache problem Euler function elementary method.
Mingshun Yang
Department of Mathematics, Weinan Teachers College Weinan, 714000, P.R.China
国际会议
西安
英文
117-119
2008-03-21（万方平台首次上网日期，不代表论文的发表时间）