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 [SOLVED] Factorials are never powers

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Bruno
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PostSubject: [SOLVED] Factorials are never powers   Sun Dec 20, 2009 4:18 pm

Show that N! is not a power of some integer, for N>1. (Obviously I'm not talking about a first power.)


Last edited by Bruno on Thu Dec 24, 2009 1:59 am; edited 1 time in total
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Mohammad
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PostSubject: Re: [SOLVED] Factorials are never powers   Wed Dec 23, 2009 4:05 pm

If p be the biggest prime number less than N then it has power 1 in prime decomposition of N! otherwise using the fact there is a prime number between p and 2p you can find a greater prime number than p. Exclamation
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Bruno
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PostSubject: Re: [SOLVED] Factorials are never powers   Thu Dec 24, 2009 1:59 am

Yes! Bertrand's postulate strikes again. Very Happy
Good job Mo.
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