关于数论函数方程S(SL(n^2))=φ_2(n)解的讨论

Solvability of Arithmetic Function Equation S( SL( n^2) ) = φ_2( n)

对于任意正整数n、S(n)、SL(n)、φ(n)分别是Smarandache函数、Smarandache LCM函数和Euler函数。利用S(n)、SL(n)、φ(n)的基本性质结合初等的方法,推广了方程S(SL(n))=φ(n),研究了S(SL(n^2))=φ_2(n)的可解性。给出并证明了上述方程的所有正整数解。

For any positive integer n,S(n),SL(n),φ(n)is Smarandache function,Smarandache LCM function and Euler function.In the present paper,the equation S(SL(n))=φ(n)were promoted,and the solvability of equation S(SL(n2))=φ2(n)was studied and all the positive integer solutions of the equation were given by using the property of S(n),SL(n),φ(n)and elementary method.