A very belated response. Not squares, but related. Using Triangular numbers. 1 3 6 10 15 21 T[3] = 3! T[3] + T[6] = 4! T[14]+T[5] = T[15] = 5! T[45] + T[89] = 7! T[210] + T[825] = 9! T[1770] + T[2030] = 10! T[71504] + T[85680] = 13! T[213384] + T[1603064] = T[299894] + T[1589154] = 15! I don't see an easy way to extend these. The density of triangular numbers seems to be sufficient for extended solutions. --Ed Pegg Jr Date: Mon, 3 Jul 2006 11:44:20 -0600 (MDT) From: Richard Guy <rkg@cpsc.ucalgary.ca> Reply-To: math-fun <math-fun@mailman.xmission.com> To: Number Theory List <NMBRTHRY@listserv.nodak.edu>, Math Fun <math-fun@mailman.xmission.com> Subject: [math-fun] Factorial n Presumably 0! = 1! = 0^2 + 1^2. 2! = 1^2 + 1^2 6! = 12^2 + 24^2 are the only integer solutions of n! = x^2 + y^2 but is there a proof? R.