2010•Unpublished venueRequires access

An equation involving Euler-totient function

Chengliang Tian

Abstract

For any positive integer n,we define the arithmetical functionΩ(n) asΩ(1) = 0;If n1 andn=p_1~(α1)p_2~(α2)...p_k~(αk) be the prime powers factorization of n,thenΩ(n) =Σ_(i=1)~kα_i.φ(n) denotes the Eulertotientfunction.The main purpose of this paper is using the elementary to study the solutions of the equationφ(φ(n)) = 2~(Ω(n)),and give all positive integer solutions.Namely,the problem proposed by before scholar issolved completely.

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Key concepts: Euler's totient function, Arithmetic function, Mathematics, Integer (computer science), Factorization, Euler's formula, Prime factor, Prime (order theory)