Bruno Admin
Posts : 184 Join date : 20090915 Age : 32 Location : the infinite, frictionless plane of uniform density
 Subject: [SOLVED] Euler's phi function Mon Nov 09, 2009 1:18 am  
 Show that the infimum of Phi(n)/n is 0.
(My estimate of the difficulty : 6/10)
Last edited by Bruno on Tue Nov 17, 2009 12:08 am; edited 1 time in total 

Jim Pythagoras
Posts : 17 Join date : 20091109
 Subject: Re: [SOLVED] Euler's phi function Sun Nov 15, 2009 5:07 pm  
 I like that you have edited the difficulty. Now that I have seen the proof on Wikipedia I don't know why I couldn't get it. I didn't think to take the reciprocal and bound it by the harmonic series. 

Bruno Admin
Posts : 184 Join date : 20090915 Age : 32 Location : the infinite, frictionless plane of uniform density
 Subject: Re: [SOLVED] Euler's phi function Sun Nov 15, 2009 5:44 pm  
 Hey Jim! So the proof is on Wikipedia! Somebody has thought of the problem before me. I think Euler used that (11/2)(11/3)(11/5)... > 0 to first show that 1/2 + 1/3 +... diverges. 

Bruno Admin
Posts : 184 Join date : 20090915 Age : 32 Location : the infinite, frictionless plane of uniform density
 Subject: Re: [SOLVED] Euler's phi function Mon Nov 16, 2009 11:12 pm  
 Those of you who would like to see the solution in full, click here. I posted the problem a not long ago on this other forum and you can find the solution there. 

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 Subject: Re: [SOLVED] Euler's phi function  
 
