Find three different positive integers whose factorials are each one less than a perfect square, such that the total of all three factorials is also a perfect square.
4! = 24 + 1 = 25 = 5**2
5! = 120 + 1 = 121 = 11 ** 2
7! = 5040 + 1 = 5041 = 71 ** 2
24 + 120 + 5040 = 5184 = 72 ** 2
This would be the answer, assuming "total" means sum, as in Cogito ergo sum. Fortunately this works, since I found no other factorials with the property of being one less than a square until exceeding the precision of my computer/calculator (roughly 2**32 or 10*18 (somewhere around 20!).
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