J4 ›› 2012, Vol. 50 ›› Issue (05): 859-862.

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Some Equations Involving Euler Function (n)

SUN Cuifang, CHENG Zhi   

  1. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui Province, China
  • Received:2011-12-09 Online:2012-09-26 Published:2012-09-29
  • Contact: SUN Cuifang E-mail:cuifangsun@163.com

Abstract:

For any positive integer n, let (n) be Euler function and Ω(n) denote the total number of prime factors of n, we studied the solutions of three kinds of equations n-(n)=2Ω(n), n-((n))=2Ω(n) and (n-(n))=2Ω(n) using the methods of number theory, obtaining all the positive integer solutions of these kinds of equations.

Key words:  Euler function (n), equation, positive integer solutions

CLC Number: 

  • O156.4