n!+1n!+1 being a perfect square

One observes that
4!+1=25=52, 5!+1=121=112
is a perfect square. Similarly for n=7 also we see that n!+1 is a perfect square. So one can ask the truth of this question:

  • Is n!+1 a perfect square for infinitely many n? If yes, then how to prove.

Answer

This is Brocard’s problem, and it is still open.

http://en.wikipedia.org/wiki/Brocard%27s_problem

Attribution
Source : Link , Question Author : Community , Answer Author :
user940

Leave a Comment