parmenides51 wrote: A function $f$ defined on integers such that $f (n) =n + 3$ if $n$ is odd $f (n) = \frac{n}{2}$ if $n$ is even If $k$ is an odd integer, determine the values for which $f (f (f (k))) = k$. $f(f(f(4n+1)))=n+1$ $f(f(f(4n+3)))=2n+6$ And so only odd solution of $f(f(f(k))=k$ is $\boxed{k=1}$