Talk:Euclid–Euler theorem

Euclid–Euler theorem has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: July 7, 2021. (Reviewed version).

A fact from Euclid–Euler theorem appeared on Wikipedia's Main Page in the Did you know column on 31 July 2021 (check views). The text of the entry was as follows:

Did you know... that after Euclid proved that every Mersenne prime leads to an even perfect number, it took more than 2000 years before Leonhard Euler proved that every even perfect number comes from a Mersenne prime?

A record of the entry may be seen at Wikipedia:Recent additions/2021/July. The nomination discussion and review may be seen at Template:Did you know nominations/Euclid–Euler theorem.

Wikipedia

GA Review

This review is transcluded from Talk:Euclid–Euler theorem/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Horsesizedduck (talk · contribs) 16:36, 5 July 2021 (UTC)[reply]

Greetings! Picking up this article for review! Number theory + Euler, what is there not to love? Horsesizedduck (talk) 16:36, 5 July 2021 (UTC)[reply]

Rate	Attribute	Review Comment
1. Well-written:
	1a. the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct.	Passes. Will give suggestions for improvements, as appropriate.
	1b. it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation.
2. Verifiable with no original research:
	2a. it contains a list of all references (sources of information), presented in accordance with the layout style guideline.	Only possible issue would be the statement section. Will confer with nominator.
	2b. reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose).	Looks set to pass. Could use a more current source, or maybe some rewording in a part mentioned in recommendations.
	2c. it contains no original research.	The nominator is indeed a notable mathematician, but no OR takes place here.
	2d. it contains no copyright violations or plagiarism.	Not a problem.
3. Broad in its coverage:
	3a. it addresses the main aspects of the topic.	Quickly addresses the proof of the theorem. Lays a proper base for any future additions, though I wouldn't know what would more there would be to say on this theorem.
	3b. it stays focused on the topic without going into unnecessary detail (see summary style).	Very focused and efficient.
	4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each.	Not a very contentious topic. Neutral coverage.
	5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute.	Nominator is the main contributor.
6. Illustrated, if possible, by media such as images, video, or audio:
	6a. media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content.	To be changed if images are inserted of course...
	6b. media are relevant to the topic, and have suitable captions.	Number theory is as unfriendly to images as it gets, I believe
	7. Overall assessment.

@David Eppstein: Making quick progress with this review, will leave suggestions here as they arise. Horsesizedduck (talk) 17:06, 5 July 2021 (UTC)[reply]

Recomendations

There is no link to the "prime numbers" article throughout, even though opportunities are abundant. Maybe the statement section would be a proper position?
- Linked in the second sentence. —David Eppstein (talk) 22:06, 6 July 2021 (UTC)[reply]
Perhaps it could start with something like, "In Mathematics, specifically number theory (maybe wikilinked?) the Euclid-Euler theorem..."
- I tend not to like articles that start "Long ago, in a galaxy far away, something vague and irrelevant maybe describing this topic, we'll get there eventually, maybe, if you have enough patience to keep reading, the Euclid-Euler theorem...". And I think the boilerplate formula "In field, X" that so many articles use is lazy writing and not actually great prose. But we should probably at least say that this is number theory. Maybe replace the current start by "The Euclid–Euler theorem is a theorem in number theory" and have good faith that anyone who recognizes the words "theorem" and "number" is capable of recognizing that it's mathematics? —David Eppstein (talk) 22:06, 6 July 2021 (UTC)[reply]
  - A good solution. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)[reply]
It may be worth noting explicitly that $2 p-1 (2 p - 1)$ is a triangular number: $M p (M p + 1) / 2$ . Pasmao (talk) 06:19, 16 October 2024 (UTC)[reply]

History

"... prime (Euclid, Prop. IX.36)" It may be better to replace with a ref or a note
- Moved into the footnote at the end of the paragraph. —David Eppstein (talk) 22:09, 6 July 2021 (UTC)[reply]
"Dickson's proof, in particular, is commonly used in textbooks" The reference that claims this is from 1981 if I am not mistaken. Is it current?
- I don't know why it wouldn't be, but I'm really not sure. It's the most recent reference I know that makes this comparison.
  - If we are both uncertain, possible solutions are rephrasing ("... saw common use in textbooks"?), omitting, or investigating further (not really sure how to do this, perhaps searching lots of book indexes? A drag/questionable use of time...) Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)[reply]
    - I changed "is" to "has been" to indicate that it once was true but might not still be. —David Eppstein (talk) 06:13, 7 July 2021 (UTC)[reply]
Considering the use of P as the letter for the sum of the series, I am wondering if there might not be a better alternative, considering that p is already in use in the expressions 2^p − 1 and 2^p − 1. Thoughts?
- Do you think it would be less confusing to just use lowercase p and t? It is more or less the same p as in all those other expressions, so I'm not sure why it needs a different name. —David Eppstein (talk) 22:10, 6 July 2021 (UTC)[reply]
  - Valid. Will defer to your opinion. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)[reply]
    - Oh wait, it's not p, it's the bigger prime 2^p-1. I guess that's why I was using the bigger P (I don't remember for sure). But I agree that p and P are too similar-looking, especially with the distortions of the math templates. I'll try switching to q and t. —David Eppstein (talk) 06:16, 7 July 2021 (UTC)[reply]

Proof

Maybe the first sentence should go like "... relies on the use of the sum of divisors function [short description of the function-sums all divisors of a number to the number]. A number is perfect if and only if its sum of divisors is twice its value." and introduce the multiplicative property in the following "Sufficiency" section.
- I think it's really the multiplicative property that's important, and made the proof possible for Euler when it wasn't for Euclid, not just the idea that summing the divisors is a function. —David Eppstein (talk) 22:13, 6 July 2021 (UTC)[reply]
  - OK. It was more a phrasing concern than a mathematical one. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)[reply]

For now, I believe this is enough. Please ping if I was unclear. Horsesizedduck (talk) 22:05, 5 July 2021 (UTC)[reply]

Placing it on hold while waiting for response. Horsesizedduck (talk) 13:56, 6 July 2021 (UTC)[reply]

Am dealing with a situation that reduces my available time on Wikipedia. Will continue to consider the article. Should finish by end of week. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)[reply]

Final remarks

Passing the article. It's clearly in better hands than mine, and seems to pass all criteria. Horsesizedduck (talk) 17:46, 7 July 2021 (UTC)[reply]

Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by MeegsC (talk) 15:10, 27 July 2021 (UTC)[reply]

(

Comment or view
Article history

)

... that after Euclid proved that every Mersenne prime leads to an even perfect number, it took over 2000 years before Leonhard Euler proved that every even perfect number comes from a Mersenne prime? Source: Pollack & Shevelev, "On perfect and near-perfect numbers", DOI:10.1016/j.jnt.2012.06.008: "It is interesting that 2000 years passed before the next important result in the theory of perfect numbers."

Reviewed: Women's National Basketball Players Association

Improved to Good Article status by David Eppstein (talk). Self-nominated at 00:30, 8 July 2021 (UTC).[reply]

hideReviewer's template for easy copy+paste

Blank template:

General: Article is new enough and long enough
New enough: Long enough:

Policy: Article is sourced, neutral, and free of copyright problems
Adequate sourcing: Neutral: Free of copyright violations, plagiarism, and close paraphrasing:

Hook: Hook has been verified by provided inline citation
Cited: Interesting:

QPQ: Done.

Overall: Article received a GA status and hook is interesting. So, DYK is good to go. Paradise Chronicle (talk) 20:15, 25 July 2021 (UTC)[reply]