Wikipedia:Articles for deletion/Kunerth's algorithm

Kunerth's algorithm

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Reason

The first reason I believe the page should be removed is non-notability. There are only two non-forum references I can find not written by the Wikipedia article's creator and main contributor about Kunerth's algorithm. (Both references are listed in the Wikipedia article.) The first is the original 1878 paper by Kunerth^[1]. It is written in German, a language neither me nor the article's creator can read (as they admitted in the talk page). The second reference is a 1920 textbook^[2]. The reference to Kunerth's algorithm in the textbook is fairly short (shorter than the body of the article), and is mostly just a restatement and very terse summary of Kunerth's original paper, with no proofs. In my opinion, an algorithm that finds modular square roots isn't notable on its own anymore because there already multiple, well known algorithms the solve the modular square root problem. (There are four Wikipedia articles on different algorithms that solve the problem.) Admittedly, the claim that $N$ doesn't need to be factored is different from the other algorithms, and may warrant notability. However, the 1920 textbook directly contradicts this claim (it states that $N$ must be prime). So, there seems to be only two relevant references to Kunerth's algorithm, one written in a language neither I nor the article's creator can read, and the other which directly contradicts one of the main claims in the article.

The second reason I'm nominating this Wikipedia page for deletion is because the most of the page is incomprehensible, low quality, and probably not correct. The algorithm as written does not work. There are many variables that aren't defined. (For example, what are $A$ and $C$ ?). As noted before me on the talk page, it seems like $w$ can be anything. There is no indication as to how the algorithm works when a square root doesn't exist (i.e., if there are no solutions $y$ to the congruence $y^{2}\equiv B\mod N$ ). There is no attempt at a proof of correctness, or even an attempt to explain why the algorithm works. While the main contributor has posted many examples of Mathematica I/O (input/output) on the talk page, there seems to be no code (pseduo or otherwise) that actually implements the algorithm in general. Two other user before me also had concerns about the algorithm presented in the article, and in neither case, were these concerns resolved by the article's main contributor.

Most of the concerns addressed in the previous paragraph could theoretically be addressed and fixed. However, as stated in the first paragraph, I don't believe that Kunerth's algorithm is notable enough and too few references on the topic seems to be available. Obviously, I don't feel comfortable fixing the article unless other references on Kunerth's algorithm are found, due to the language barrier of the original paper and the lack of other English references. Regardless, the state of the current article needs to be addressed.

For more context, see the discussion I started on it's talk page: Talk:Kunerth's_algorithm#This_article_should_be_deleted. Also, here is another user attempting to understand the algorithm presented directly on the main contributor's talk page: User_talk:Endo999#A_question_about_Kunerth’s_algorithm_on_how_to_get_several_square_root_for_the_same_square….

Also, as a disclaimer. I'm not an active Wikipedia contributor, so I welcome any feedback about my approach to nominating an article for deletion. byhill (talk) 04:33, 1 May 2025 (UTC)[reply]

The article is noteable as it has two pages devoted to it in the 1920 History of Numbers by Leonard Dickson, who was the premiere American mathematician between 1900 and 1950. Saying that Dickson's reference is 100 years old is like saying that Dante wrote in 1300 and his thought does not reflect Catholic church dogma. It does and so similarly is Dickson's expertise in Number theory (1920) to be respected. Endo999 (talk) 04:48, 1 May 2025 (UTC)[reply]
The Kunerth modular square root algorithm is notable as it is the only one I know of that manages to find the square root of a number without factoring the

modulus. For that alone it is notable. The algorithm substitutes the requirement that a quadratic equation must be solved for the need to factor the modulus. It can do this for modula that cannot be factored. Endo999 (talk) 15:42, 1 May 2025 (UTC)[reply]
The Dickson source talks only about prime moduli. If you know that the modulus is prime you know its prime factorization. So there is no avoidance of factoring. —David Eppstein (talk) 16:25, 1 May 2025 (UTC)[reply]

References

^ Adolf Kunerth, "Sitzungsberichte. Academie Der Wissenschaften" vol 78(2), 1878, p 327-346, url="https://pdfhost.io/v/~OwxzpPNA_KUNERTH_1878" retrieved="30/05/2025"
^ Leonard Eugene Dickson, "History of Numbers", vol 2, pp. 383–384.

Those pages of Dickson are readable here: [1]. Reading them, it becomes obvious that Kunerth's work is primarily about finding integer solutions $(x,y)$ to the quadratic equation $y^{2}=ax^{2}+bx+c$ . Modular square roots, for prime moduli only, are mentioned in one paragraph as a special case of this method for $a=0$ and modulus $b$ . It does not really support the case made by our article that something called "Kunerth's algorithm" is a general method for finding modular square roots, and having a single secondary source on this method (whatever the method actually is determined to be) is not enough for WP:GNG-based notability. —David Eppstein (talk) 05:43, 1 May 2025 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. –LaundryPizza03 (d c̄) 08:41, 1 May 2025 (UTC)[reply]

Delete, per byhill and Eppstein. Also, looking on the talk page of the article, it appears, that the editor wrote a computer implementation, made some tests, and tried to (poorly) describe their implementation in this article. This is WP:Original research, and does not belong to Wikipedia. D.Lazard (talk) 08:47, 1 May 2025 (UTC)[reply]

[1] Adolf Kunerth, "Sitzungsberichte. Academie Der Wissenschaften" vol 78(2), 1878, p 327-346, url="https://pdfhost.io/v/~OwxzpPNA_KUNERTH_1878" retrieved="30/05/2025"

[2] Leonard Eugene Dickson, "History of Numbers", vol 2, pp. 383–384.

[1]

[2]