Determine all pairs of positive integers $(m,n)$ such that m is but divisible by every integer from $1$ to $n$ (inclusive), but not divisible by $n + 1, n + 2$, and $n + 3$.
Source: 2006 MOP Homework Red NT 2
Tags: number theory, divisible
Determine all pairs of positive integers $(m,n)$ such that m is but divisible by every integer from $1$ to $n$ (inclusive), but not divisible by $n + 1, n + 2$, and $n + 3$.