Are there any natural numbers $n$ such that $\phi (n) = n$?
The function $\phi(n)$ counts the natural numbers from 1 to $n$ which are coprime to $n$.
For $n>1$, we have $\gcd(n,n) = n \ne 1$, and so $\phi(n) < n$.
The only remaining case is $n=1$, and indeed $\phi(1)=1$.