# Talk:Euclid–Euler theorem

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)

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

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

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)
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)
A good solution. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)
It may be worth noting explicitly that 2p-1(2p − 1) is a triangular number: Mp (Mp + 1) / 2. Pasmao (talk) 06:19, 16 October 2024 (UTC)


### 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)
"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)
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)
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 2p − 1 and 2p − 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)
Valid. Will defer to your opinion. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)
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)


### 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)
OK. It was more a phrasing concern than a mathematical one. Horsesizedduck (talk) 22:55, 6 July 2021 (UTC)
For now, I believe this is enough. Please ping if I was unclear. Horsesizedduck (talk) 22:05, 5 July 2021 (UTC)
Placing it on hold while waiting for response. Horsesizedduck (talk) 13:56, 6 July 2021 (UTC)
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)

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)