Problem

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: algebra, Functional Equations



Determine all functions $f:\mathbb{Z} \rightarrow \mathbb{Z}$ which satisfy the following equations: a) $f(f(n))=4n+3$ $\forall$ $n \in \mathbb{Z}$; b) $f(f(n)-n)=2n+3$ $\forall$ $n \in \mathbb{Z}$.