Problem

Source: 14-th Iranian Mathematical Olympiad 1996/1997

Tags: function, algebra proposed, algebra



Determine all functions $f : \mathbb N_0 \rightarrow \mathbb N_0 - \{1\}$ such that \[f(n + 1) + f(n + 3) = f(n + 5)f(n + 7) - 1375, \qquad \forall n \in \mathbb N.\]