### Abstract

Original language | English |
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Pages (from-to) | 12-14 |

Number of pages | 3 |

Journal | African Journal of Mathematics and Computer Science Research |

Volume | 9 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 |

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*African Journal of Mathematics and Computer Science Research*, vol. 9, no. 2, pp. 12-14. https://doi.org/10.5897/AJMCSR2016.0648

**Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1).** / Mothebe*, Mbakiso Fix; Samuel, Sebaameng.

Research output: Contribution to journal › Article

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

VL - 9

SP - 12

EP - 14

JO - African Journal of Mathematics and Computer Science Research

JF - African Journal of Mathematics and Computer Science Research

SN - 2006-9731

IS - 2

ER -