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Some Results on the Unitary Analogue of the Lehmer Problem  
 
  Authors: Marta Skonieczna,  
  Keywords: Lehmer problem, Unitary analogue of Lehmer problem.  
  Date Received: 10/04/08  
  Date Accepted: 29/05/08  
  Subject Codes:

11A25.

  
  Editors: Jozsef Sandor,  
 
  Abstract:

Let $ M$ be a positive integer with $ Mge 4$, and let $ varphi^*$ denote the unitary analogue of Euler's totient function $ varphi$. Using Grytczuk-Wójtowicz's techniques from the paper [2] we strengthen considerably the lower estimations of the solutions $ n$ of the equation $ Mvarphi^*(n)=n-1$. Moreover, we show that the set of positive integers, which do not fulfil this equation for any $ Mge 2$, contains an interesting subset generated by Ramsey's theorem. ;


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