Given that a, b, and c are positive integers solve the following equation.
a!b! = a! + b! + c^2
the question is complete. I know you are thinking of 3 variables but 1 equation. But this question is solvable.
by trial and error, a=2, b=3, c=2.
But my concern is, is there any other way that can be used to solve it, systematically and algebraically?
My thought : Try to relate the multiplication of 2 factorials and their sums.