方程φ(kn)=φ((k+1)n),(k=1,2,…)的正整数解

The positive integer solution to the equation φ (kn) = φ ((k+1) n), (k = 1, 2, ...)

φ (m)是Euler函数。本文根据Euler函数的性质 ,给出了方程 φ (kn) =φ ((k +1 )n) ,(k =1 ,2 ,… )解的存在性 ,并推广到更为一般的结果 :方程 φ (k1n) =φ (k2 n) (k1,k2 均为自然数 )解的存在性。

m) is Euler function. This paper first presents the existence of solution to the equation φ (kn) = φ ( (k+1) n), (k = 1, 2, ...) according to the property of the Euler function, then proceeds to generalize it into the existence of solution to the equation φ (k1n) = φ (k2n) (both k1 and k2 being natural numbers).