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Numbers n such that there exist x, y with n^2 = x! + y!.
2

%I #15 Sep 03 2023 19:53:08

%S 2,5,11,12,71

%N Numbers n such that there exist x, y with n^2 = x! + y!.

%C a(6) > 10^78. - _Sascha Kurz_, Mar 24 2002

%C a(6) > 10^1545. - _Robert G. Wilson v_, Apr 06 2006

%C a(6) > 10^10000. - _Sean A. Irvine_, Sep 03 2023

%H Lev Emelyanov, <a href="http://forumgeom.fau.edu/POLYA/Inventory/Inventory015.html">Square as sum of two factorials</a>

%e 2^2 = 2!+2!; 5^2 = 4!+1!; 11^2 = 5!+1!; 12^2 = 5!+4!; 71^2 = 7!+1!.

%t Sqrt@ Select[ Sort@ Flatten@ Table[x! + y!, {x, 650}, {y, x}], IntegerQ@ Sqrt@ # &] (* _Robert G. Wilson v_, Apr 06 2006 *)

%K nonn

%O 1,1

%A Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Nov 23 2001