纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
6期
564-568
,共5页
Euler函数%方程%正整数解
Euler函數%方程%正整數解
Euler함수%방정%정정수해
Euler′s totient function%equation%positive integer solutions
对任意的正整数 n,函数?(n)为著名的 Euler 函数,即在序列1,2,···, n 中与n 互质的整数的个数。本文利用初等方法研究了方程?(?(x))的可解性,并给出了该方程的全部正整数解。
對任意的正整數 n,函數?(n)為著名的 Euler 函數,即在序列1,2,···, n 中與n 互質的整數的箇數。本文利用初等方法研究瞭方程?(?(x))的可解性,併給齣瞭該方程的全部正整數解。
대임의적정정수 n,함수?(n)위저명적 Euler 함수,즉재서렬1,2,···, n 중여n 호질적정수적개수。본문이용초등방법연구료방정?(?(x))적가해성,병급출료해방정적전부정정수해。
The function ?(n) is the famous Euler’s totient function for arbitrary positive integer n, i.e. it is the integral individual number of coprime with in the sequence 1, 2, · · · , n?1, n. In the present paper, the solvability of equation?(?(x))=2t was studied and all the positive integer solutions of the equation were given by using the elementary methods.
