关键词: Euler函数(n), 方程, 正整数解

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)=2^Ω(n), n-((n))=2^Ω(n) and (n-(n))=2^Ω(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