"Surprise!" said c
Number Theory
Level
4
\[\displaystyle \large a!b! = a! + b! + c^2\]
Positive integers \(a\), \(b\), and \(c\), with \(a > b\), are the unique solution to the equation above.
If \(\dfrac {a^b}{c} = \dfrac mn\) for coprime positive integers \(m\) and \(n\), find \(m + n\).
by
Zach Abueg