Find all functions  $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that  $f(2n)+2f(2m)=f(f(n+m))$,   $\forall m,n\in \mathbb{Z}$

Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(2n)+2f(2m)=f(f(n+m))$, $\forall m,n\in \mathbb{Z}$.

  • There is a typo: f(2n)+2f(m)=f(f(n+m))

  • just for clarification you're saying that the typo, that is the *incorrect* relation is: f(2n)+2f(2m)=f(f(n+m)), and that the CORRECT relation is: f(2n)+2f(m)=f(f(n+m))?

  • Yes

Answer

PDF attached

  • Thank you so much. This is amazing.

The answer is accepted.