The conversation between human and AI assistant.
Is n! ever a perfect square?
Got it. So back to the main question, is n! ever a perfect square?
No, n! is never a perfect square when n is greater than 1. This has been proven in mathematics and is known as Brocard's Problem. However, there are some special cases for n=1 and n=4 where n! is a perfect square (1! and 4!, respectively).