MathNet 2010 — Part 04 Question 106

Let $m \in \mathbb{N}$. $m^2 \lt a, b \lt m^2 + m$ and $a \neq b$. Find all the natural $c$, such that $c \mid ab$, $m^2 \lt c \lt m^2 + m$.

(proposed by D. Ganzorig)