Let be the product of positive integers which are and relatively prime to . Prove that

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- Dec 7th 2009, 01:38 AMChandru1Arithmetical functions
Let be the product of positive integers which are and relatively prime to . Prove that

- Dec 7th 2009, 04:01 AMPaulRS
Let

Then (see here )

Thus, by Möbius inversion formula: (1)

Now:

Then taking exponentials in (1) your identity follows. - Dec 8th 2009, 03:47 AMChandru1superb
Hi--

Paul, that was a superb answer. I really liked the proof. By the way i am just a beginner in analytic number theory and i am finding this a bit difficult as i am learning it on my own. Difficulty not in the proofs or theorems but in solving problems.

Like, i couldn never have considered the way you taken F(n). I mean how did u get the idea...

Pls help..i really want to master number theory as its such a wonderful subject....