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.

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