Find all prime numbers $p$ such that $ p = m^2 + n^2$ and $p\mid m^3+n^3-4$.
Problem
Source: Iranian National Olympiad (3rd Round) 2004
Tags: number theory proposed, number theory
Source: Iranian National Olympiad (3rd Round) 2004
Tags: number theory proposed, number theory
Find all prime numbers $p$ such that $ p = m^2 + n^2$ and $p\mid m^3+n^3-4$.