When is n! a perfect square?
Level
pending
Find the sum of all natural numbers n such that, n! is a perfect square.
The answer is 1.
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1 solution
By bertrand's postulate,we know there exist a prime between n and 2n-2 for n >3.So,n! will have a prime with the power of 1 in it for n ≥ 7 .
Hence,we only need to consider first few values of n,which can be done by hand.