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 [SOLVED] Euler's phi function

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Bruno
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PostSubject: [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
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Jim
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PostSubject: 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.
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Bruno
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PostSubject: 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. Sad

I think Euler used that (1-1/2)(1-1/3)(1-1/5)... --> 0 to first show that 1/2 + 1/3 +... diverges.
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Bruno
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PostSubject: 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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