African Journal of Mathematics and Computer Science Research
Subscribe to AJMCSR
Full Name*
Email Address*

Article Number - 42FFD3C59708


Vol.9(2), pp. 12-14 , July 2016
DOI: 10.5897/AJMCSR2016.0648
ISSN: 2006-9731



Short Communication

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



Mbakiso Fix Mothebe*
  • Mbakiso Fix Mothebe*
  • Department of Mathematics, University of Botswana, Pvt Bag 00704, Gaborone, Botswana.
  • Google Scholar
Sebaameng Samuel
  • Sebaameng Samuel
  • Department of Mathematics, University of Botswana, Pvt Bag 00704, Gaborone, Botswana.
  • Google Scholar







 Received: 25 April 2016  Accepted: 20 July 2016  Published: 31 July 2016

Copyright © 2016 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0


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.

Burton DM (2002). Elementary Number Theory. McGraw-Hill, International Editions.

 

Mothebe MF, Modise BT (2016). An extension of the Euler Phi-function to Sets of Integers Relatively Prime to 30. J. Math. Res. 8(2):45-48. 
Crossref

 


APA Mothebe, M. F., & Samuel, S. (2016). Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1). African Journal of Mathematics and Computer Science Research, 9(2), 12-14.
Chicago Mbakiso Fix Mothebe and Sebaameng Samuel. "Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)." African Journal of Mathematics and Computer Science Research 9, no. 2 (2016): 12-14.
MLA Mbakiso Fix Mothebe and Sebaameng Samuel. "Properties of the Euler phi-function on pairs of positive integers (6x - 1, 6x + 1)." African Journal of Mathematics and Computer Science Research 9.2 (2016): 12-14.
   
DOI 10.5897/AJMCSR2016.0648
URL http://academicjournals.org/journal/AJMCSR/article-abstract/42FFD3C59708

Subscription Form