Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)

African Journal of Mathematics and Computer Science Research

Mbakiso Fix Mothebe*¹ 

关键词: Euler phi-function;    multiplicative function.;   

DOI  :  10.5897/AJMCSR2016.0648

学科分类：计算机科学（综合）

来源: Academic Journals

【 摘 要 】

Let n ≥ 1 be an integer. Define ϕ2(n) to be the number of positive integers x, 1 ≤ x ≤ n, for which both 6x−1 and 6x+1 are relatively prime to 6n. The primary goal of this study is to show that ϕ2 is a multiplicative function, that is, if gcd(m, n) = 1, then ϕ2(mn) = ϕ2(m)ϕ2(n).

【 授权许可】

CC BY