Prove that $n!$ can never be a perfect square for $n>1$
I have no idea on how to begin this problem.(I don't want to use Bertrand's theorem as it is beyond the level of the exam I have to take now.)
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1what other properties do you know ? – Feb 06 '20 at 13:57
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I doubt that we can prove the claim without Betrand's postulate. – Peter Feb 06 '20 at 13:57
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See this comment on an old question – lioness99a Feb 06 '20 at 13:58
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1Specifically I know most of pre college stuff – Arjun Feb 06 '20 at 13:58
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how about the number of 2's in the factorization ? if you know that you can rule things out ... – Feb 06 '20 at 14:00