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# [SOLVED] Factorials are never powers

AuthorMessage

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 Subject: [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

Descartes

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 Subject: 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.

Posts : 184
Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

 Subject: Re: [SOLVED] Factorials are never powers   Thu Dec 24, 2009 1:59 am Yes! Bertrand's postulate strikes again. Good job Mo.