Bruno
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Age : 36
Location : the infinite, frictionless plane of uniform density
![[SOLVED] Factorials are never powers Empty](https://2img.net/i/empty.gif) | | 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 | |
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Mohammad
Descartes
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Join date : 2009-11-05
Age : 40
Location : Right behind you
| | 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.  | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
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. | |
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