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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.
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The article has used φ for a long time. Please leave it like it is, changing notation is pointless and bound to produce heated and sterile arguments. There were 4 uses of ϕ instead of φ, I changed them for consistency, as φ is overwhelmingly more common in the article. Note that both are lowercase
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We generally only include proof outlines, and not full proofs, for most articles. Proofs are typically included only when they are particularly enlightening, and not merely as a way to verify a mathematical truth. In most cases, an outline suffices for that. For verification, we can point to
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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.
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I think it would be better is a full proof for the multiplicity of the totient function is furnished in this page. If someone disagrees, please say so. I will put up the proof 3 days after this message is posted if there is no
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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
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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)? --
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Perhaps your browser is rendering the characters differently than mine? For me {{math|''φ''(''n'')}} gives me the loopy character φ(n), or in math mode
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I think it is imperative that this article choose a consistent notation for phi. This has been mentioned before on the talk page (
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says (and not related in any way to the Greek letter Φ), but inspired by the letter Ø in the
Norwegian and Danish alphabets.
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The other reference for the same claim, "Bordellès in the external links", refers to a long-removed deadlink, archived at
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correctly in all cases. Doesn't matter, we need it to render correctly for all readers, and apparently only <math: -->
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There is a new reference (currently #25) to StackExchange. StackExchange is not considered a reliable source.
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Thanks for making the change! I am more concerned with consistency than which version was ultimately chosen.
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Yes, I will change to math mode: I don't get at all what you describe (I am on MacOS Big Sur)! Thank you! --
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There is a proof outline. I think that with a little more explanation, it could become a full proof.
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is that phi is small case, couldn't categorize on that font whether it is lower or upper alphabet.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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but possibly not in the right version, which as an open forum also looks non-reliable. —
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I didn't know how to flag content for review, so I posted on the talk page.
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I agree with showing the two ways it is commonly written.
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Maybe we can see through
Article, and make reference of
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mathematical publications that contain the proofs. —
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718:{\displaystyle \varphi (n)}
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