Talk:Proofs involving the totient function

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This article was nominated for deletion on 10 December 2007. The result of the discussion was keep.

	*On 16 December 2007, Proofs involving the totient function* was linked from Slashdot, a high-traffic website.** All prior and subsequent edits to the article are noted in its revision history.

1 Explanation of proof step in inequalities?
2 Expert required
3 Number of integers up to n and prime to a given m
4 Requested move
5 Citations

[edit] Explanation of proof step in inequalities?

I don't quite understand this step in the proof in the inequality section:

$\prod_{i=1}^k \left( 1 - \frac{1}{p_i} \right)^{-1} > \sum_{m=1}^{p_k} \frac{1}{m}$

Why is it true? I tried several different things but they didn't come up with this. Is it based on some previous or well-known result? Thanks. Deco 00:46, 7 January 2007 (UTC)

Hello there, just use $\frac{1}{1-z} = 1 + z + z^2 + z^3 + \ldots.$ BTW, I am not sure replacing n by

n k

really improves readability. We should keep it simple. Having said what n is in the introduction to the proof should suffice. Hope this helps. -Zahlentheorie 11:08, 8 January 2007 (UTC)

[edit] Expert required

This page needs attention from an expert to write an introductory essay and preface each proof with an explanation of the strategy that will be used. -Zahlentheorie 15:51, 29 April 2007 (UTC)

Yes. There is still a bit of math obsification in the proof, there are spots where it could me made a little clearer, and slightly easier to understand. Would you qualify me as an expert if: I am an undergrad, that has taken my course work in Finite math ( got an A+ ), and advanced Finite ( got an A, this freaking class was mostly proofs and foudation stuff ), and took the graduate series class, where this theorm was presented. I took the class, at the recommendation of the Finite Math teacher! I am pursuiing this line of study for doing graduate study in Galois theory. Let me know what your opinion on qualifications is. 67.188.118.64 (talk) 08:32, 17 December 2007 (UTC)

[edit] Number of integers up to n and prime to a given m

The inclusion-exclusion argument in this proof needs to be changed to an argument involving an interchange of the order of summation, as in the orginal document. -Zahlentheorie 22:40, 28 May 2007 (UTC) Removed the proof since the one in the source document is more elegant. -Zahlentheorie 11:37, 1 June 2007 (UTC)

[edit] Requested move

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

Per Wikipedia:Subpages, this article should be named Proofs involving the Totient function, not Totient function/Proofs. I'd do the move myself, but this just hit Slashdot, so I'll just err to the side of caution here. --Phirazo 06:06, 17 December 2007 (UTC)

Woudlnt it be better to have a more grafic slashdot effect icon? 67.188.118.64 (talk) 08:35, 17 December 2007 (UTC)

The word "totient" shouldn't be capitalized. So maybe Proofs involving the totient function. --Zundark (talk) 10:58, 17 December 2007 (UTC)

Move is done. Mango juice^talk 17:23, 17 December 2007 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

The new title makes it even more clear that the topic itself isn't notable. Suggest transwiki to wikisource, assuming licensing compatibility. Dekimasuよ! 04:49, 20 December 2007 (UTC)

[edit] Citations

Would an expert please decide what to do about the citation-needed tags, of which there is one on every line of the second proof? -Zahlentheorie (talk) 23:04, 18 December 2007 (UTC)