Talk:Euler's totient function

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How to pronounce totient?—Tokek 08:15, 23 Jun 2005 (UTC)

I think it is "toe shent". BTW, I prefer "the cototient is defined as" because it is a definition, not something that happens to be true. Bubba73 15:22, 23 Jun 2005 (UTC)

Both "is defined as" and "is" are appropriate, however you actually typed "defined as is" instead of "is defined as" so it required fixing. The statement can be taken as a definition for cototient either way.—Tokek 17:24, 23 Jun 2005 (UTC)

That was a typo. "is defined as" makes it clear that it is a definition. If they're both appropriate, why not use the one that is more appropriate (is defined as)? I wrote that line originally without the "defined" part. Then I realized that it would improve the article to have "defined" in there, so I changed it, but I accidently stuck it in at the wrong place. Bubba73 18:01, 23 Jun 2005 (UTC)

Noted. —Tokek 19:06, 23 Jun 2005 (UTC)

Doesn't totient(n) always equal a positive integer? Railgun 16:59, 26 June 2006 (UTC)

What does the phrase "randomly large n" mean? Should that be "general n"? 62.8.160.190 05:17, 26 July 2006 (UTC)

1 less or equal
2 lim sup
3 other relations
4 Applications
5 Phi Function
6 Different phis

[edit] less or equal

In the definition

The totient φ(n) of a positive integer n is defined to be the number of positive integers less than n and coprime to n.

Ncik changed less that into less or equal than

As n is not coprime to n, I fail to see the improvement of this change. Ncik, please explain. Bo Jacoby 14:52, 2 December 2005 (UTC)

It makes a difference for n=1. The original definition would make the value 0, the correction makes it 1. −Woodstone 21:09, 2 December 2005 (UTC)

Is 1 really coprime to 1 ? Yes, according to definition. Thank you. Bo Jacoby 12:41, 8 December 2005 (UTC)

[edit] lim sup

there are better ways than mine to write lim sup and lim inf with bars over and under the lim respectively

can anyone do that? (User:Evilbu 4 Feb 2006)

Don't know; however, I think "lim sup" is clearer and more commonly used than symbols with lines over them. Notation should allways be clear in WP, since there are many readers from diverse backgrounds. linas 04:56, 5 February 2006 (UTC)

[edit] other relations

a useful relation is that $p h i (n) + s i g m a (n) = n * t a u (n)$ for n prime

I also believe the distance from a highly composite number to the nearest prime (or in effect the largest prime factor of the HCN) is expressible in terms of phi and tau. A crude first stab at it is $f a c t o r = l n [100 * (p h i * * K 1) / [t a u * * (1 + K 1)]] 2, K 1 = 0.55$ Applies when the prime is not immed adjacent, thru 146th HCN --Billymac00 19:54, 15 May 2006 (UTC)

[edit] Applications

What about applications of Euler's totient function? (Especially in CS)--Čikić Dragan 17:07, 16 May 2006 (UTC)

[edit] Phi Function

Can someone find phi(2695), phi(4312), and phi(5390)? They might all be the same.

They are indeed - all equal to 1680. And the significance is ... ?

[edit] Different phis

Okay, what's up with the inconsistent usage of phi? The TeX version gives $φ$ , while the HTML version gives φ. Should this article use the same phi style, or does it really matter? -Matt 17:23, 3 September 2006 (UTC)

The TeX version is an uppercase phi, Φ. The lowercase phi can also be generated, \varphi $\varphi$ . There are HTML-versions for both uppercase and lowercase phis too, Φ Φ and φ φ. I don't know for sure but I think the uppercase phi is the "official" symbol used to denote the Euler's totient function and thus that should be used. Currently all articles I have seen referring to this article unfortunately use the lowercase phi. But of course it would be simple to convert them into uppercase phis if so is agreed. --ZeroOne (talk | @) 17:33, 2 November 2006 (UTC)

The TeX \phi is not an uppercase phi; \Phi is. Both \phi and \varphi denote a lowercase phi, just differently styled. Fredrik Johansson 17:40, 2 November 2006 (UTC)

Confusing. Uppercase TeX phi: