数论函数方程φ_(2)(n)=S(SL(n ^(l)))的可解性

The solvability of arithmetic function equationφ_(2)(n)=S(SL(n ^(l)))

讨论了当l=28和l=31时数论函数方程φ_(2)(n)=S(SL(n^( l)))的可解性,并结合初等数论的方法给出其一切正整数解。其中,φ_(2)(n)为广义欧拉函数,S(n)为Smarandache函数,SL(n)为Smarandache LCM函数。

Letφ_(2)(n)be generalized Euler function,S(n)be Smarandache function and SL(n)be Smarandache LCM function,the solvability of the arithmetic function equationφ_(2)(n)=S(SL(n^(l)))at l=28,31 is studied using elementary number theory methods.All the positive integer solutions of the above two equations are obtained.