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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Euler's phi function
Multiplicative Functions
Relatively prime
Integer

Cite this

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title = "Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)",
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.",
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year = "2016",
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language = "English",
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Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1). / Mothebe*, Mbakiso Fix; Samuel, Sebaameng.

In: African Journal of Mathematics and Computer Science Research, Vol. 9, No. 2, 2016, p. 12-14.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)

AU - Mothebe, Mbakiso Fix

AU - Samuel, Sebaameng

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.5897/AJMCSR2016.0648

DO - 10.5897/AJMCSR2016.0648

M3 - Article

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JO - African Journal of Mathematics and Computer Science Research

JF - African Journal of Mathematics and Computer Science Research

SN - 2006-9731

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ER -