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

Mbakiso Fix Mothebe*, Sebaameng Samuel

Research output: Contribution to journalArticle

Abstract

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). Key words: Euler phi-function, multiplicative function.
Original languageEnglish
Pages (from-to)12-14
Number of pages3
JournalAfrican Journal of Mathematics and Computer Science Research
Volume9
Issue number2
DOIs
Publication statusPublished - 2016

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