Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that (a) $f(1)=1$ (b) $f(n+2)+(n^2+4n+3)f(n)=(2n+5)f(n+1)$ for all $n \in \mathbb{N}$. (c) $f(n)$ divides $f(m)$ if $m>n$.
Problem
Source: MOP 2005 Homework - Black Group #3
Tags: function, induction, algebra solved, algebra