The solvability of arithmetic function equation <inline-formula><tex-math id="M3">$ {\varphi }_{e}\left(n\right)=Z\left(SL\right(n\left)\right) $</tex-math></inline-formula> <inline-formula><tex-math id="M4">$ (e=\left.12\right) $</tex-math></inline-formula>

Using definition and properties of the generalized Euler function and Smarandache LCM function, this paper discusses the integer solutions problems of equations involving generalized Euler functions $ {\varphi }_{e}\left(n\right)=Z\left(SL\right(n\left)\right)(e=12) $.