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  Volume 9, Issue 2, Article 55
 
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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