hmm. Jer raises an interesting point. My solution (144, 784, 2304, etc.) does require imaginary square roots, but everything imaginary cancels out and the result is a real integer, so I'm going to take the position that n can be bigger than 625/4 and that there are an infinite number of answers.
I suppose it depends on what the definition of "Just Math" is, but I contend that imaginaries are "just numbers".
I hope pcbouhid weighs in when he posts the solution.
Imagination
