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, 5 and 7.

4! =   24 =  5² - 1
5! =  120 = 11² - 1
7! = 5040 = 71² - 1

4! + 5! + 7! = 5184 = 72²

Posted by Dej Mar on 2009-02-25 13:41:01