Talk:Euler's totient function

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Totient numbers

This section contains there are infinitely many nontotients, and indeed every odd number has an even multiple which is a nontotient, the word "even" being added by a recent edit. In both versions, this sentence is a nonsense, as every odd number greater than 1 is a nontotient; thus no need to consider multiples. I guess that the correct assertion should be every totient has a multiple (by an odd number) that is a nontotient. However this needs to be checked on the source. D.Lazard (talk) 09:59, 25 April 2015 (UTC)[reply]

As you say, odd numbers greater than 1 are trivially nontotients, so what is of interest is the existence of even nontotients. I imagine the previous writer meant "there are infinitely many even nontotients, and indeed..." but just forgot the "even". I've checked the paper and in fact it proves that any number (even or odd) has a multiple which is a nontotient. If n is odd then the nontotient multiple of 2n gives an even nontotient multiple of n, so this is equivalent to saying any number has an even nontotient multiple. I'll make those changes. Especially Lime (talk) 08:54, 20 May 2016 (UTC)[reply]

Unexplained revert of style improvement

My edit in Euler's totient function#Euler's product formula has been reverted by an IP user, without any explanation. My edit consisted in

Removing, per MOS:HEADINGS the redundant reference (through a formula) to the article title.
Replacing a heading consisting of a technical formula by a less technical phrase (the formula was redundant, as reproduced in the body
Avoiding the confusing term "modulo-and-coprime", which is nowhere defined in Wikipedia
Linking coprime

All are style improvements that does affect in any way the content of the article. As I cannot find any valid reason for rejecting these edits, I have restored them. Please, if I have missed something, please discuss here before a second revert. D.Lazard (talk) 15:52, 13 January 2017 (UTC)[reply]

Not Empty Set is that Correct - Puzzling

Empty set says (and not related in any way to the Greek letter Φ), but inspired by the letter Ø in the Norwegian and Danish alphabets.

My last month Mathematics Today Magazine from mtG has a sentence,-

"Empty set is subset of every set and every set is subset of itself. We denote by it by Φ or {}"

is that phi is small case, couldn't categorize on that font whether it is lower or upper alphabet.

And however, Φ(n) -> Phi(n) -> Euler's totient function

Maybe we can see through Article, and make reference of Empty set if it is relevance to do that as per the sentence made by mtG

—Dev A~~nand~~ Sadasivam^t@lk 02:26, 30 June 2018 (UTC)[reply]

Letter Phi in mathematics

(From my talk page, + answer, Sapphorain (talk) 22:23, 26 December 2018 (UTC))[reply]

Hello, regarding your recent revert of my edit, could you provide me an example of some respectable mathematical writing where the author would use the glyphs "φ" and "ϕ" as different variables (to denote two different things)? --Alexey Muranov (talk) 22:08, 26 December 2018 (UTC)[reply]

No I cannot, and I am not interested in finding one. But it is not the point. Two different ways of writing the same letter have been used in many instances to denote different objects. So the present precision is quite legitimate and there is no reason to suppress it. Sapphorain (talk) 22:23, 26 December 2018 (UTC)[reply]

I agree with showing the two ways it is commonly written. Bubba73 ^{You talkin' to me?} 23:25, 26 December 2018 (UTC)[reply]

Although they both refer to the Greek letter phi, the two are separate symbols. I believe they both should be shown or described. In fact, I have seen some fields of mathematics prefer one symbol to the other.—Anita5192 (talk) 23:28, 26 December 2018 (UTC)[reply]

Divisor Sum Proof Error

A line in the "Divisor Sum" portion under "Computing Euler's totient function" states "Any such k must clearly be a multiple of n/d, but it must also be coprime to d," but there are many fractions in the n = 20 example given where k is not coprime to d. For example, k = 2 and d = 10 are not coprime. I didn't know how to flag content for review, so I posted on the talk page. X9du (talk) 21:39, 3 May 2020 (UTC)X9du[reply]