Tonelli–Shanks algorithm: Revision history

9 July 2025

• curprev 01:1501:15, 9 July 2025 Taylor Riastradh Campbell talk contribs 19,020 bytes +7 →Uses: Link to Rabin signature algorithm, not to broken textbook encryption counterexample. undo

15 May 2025

• curprev 13:0213:02, 15 May 2025 212.17.33.98 talk 19,013 bytes 0 →Tonelli's algorithm will work on mod p^\lambda undo

17 February 2025

• curprev 05:1305:13, 17 February 2025 Chai T. Rex talk contribs m 19,013 bytes +19 →Generalizations: Corrected p^k to <math>p^\lambda</math> undo

22 December 2024

• curprev 00:5800:58, 22 December 2024 2601:285:4080:5960:b9e5:77a7:68d1:1366 talk 18,994 bytes +27 No edit summary undo

20 November 2024

• curprev 21:0221:02, 20 November 2024 AManWithNoPlan talk contribs 18,967 bytes +178 Altered template type. Add: isbn, pages, volume, date, series, title, chapter, authors 1-1. Changed bare reference to CS1/2. | Use this tool. Report bugs. | #UCB_Gadget undo
• curprev 17:2217:22, 20 November 2024 Bo-3903 talk contribs 18,789 bytes +51 Importing Wikidata short description: "Algorithm used in arithmetic" undo Tag: Shortdesc helper

18 January 2024

• curprev 22:1322:13, 18 January 2024 134.19.105.142 talk 18,738 bytes +7 →Speed of the algorithm undo

13 September 2023

• curprev 02:0902:09, 13 September 2023 68.203.1.10 talk 18,731 bytes +38 →Core ideas undo

11 September 2023

• curprev 05:3405:34, 11 September 2023 68.203.1.10 talk 18,693 bytes +3 →Core ideas: diction undo
• curprev 05:0505:05, 11 September 2023 68.203.1.10 talk 18,690 bytes +8 →Speed of the algorithm: linked "Legendre symbol" undo

7 September 2023

• curprev 16:1516:15, 7 September 2023 145.94.187.163 talk 18,682 bytes −10 →Core ideas undo
• curprev 16:1416:14, 7 September 2023 145.94.187.163 talk 18,692 bytes +36 →Core ideas undo

14 May 2023

• curprev 13:1113:11, 14 May 2023 Dancing Dollar talk contribs m 18,656 bytes +2 →The algorithm: clean up, typo(s) fixed: ie → i.e. undo Tag: AWB

19 April 2022

• curprev 07:0707:07, 19 April 2022 JWilk talk contribs 18,654 bytes +59 →Tonelli's algorithm will work on mod p^k: don't use asterisk as multiplication sign undo
• curprev 07:0107:01, 19 April 2022 JWilk talk contribs m 18,595 bytes +1 →Tonelli's algorithm will work on mod p^k: fix spacing undo
• curprev 07:0107:01, 19 April 2022 JWilk talk contribs 18,594 bytes −2 →Tonelli's algorithm will work on mod p^k: use \pmod undo

15 November 2021

• curprev 04:2304:23, 15 November 2021 Citation bot talk contribs 18,596 bytes +85 Add: s2cid, issue, publisher. | Use this bot. Report bugs. | Suggested by Abductive | #UCB_toolbar undo

25 March 2021

• curprev 15:4715:47, 25 March 2021 71.187.248.147 talk 18,511 bytes +51 →Uses: The quadratic sieve is a better example than Rabin's cryptosystem, which frequently sidesteps Tonelli-Shanks by restricting to the p=3 mod 4 case. The linked page on the quadratic sieve mentions Shanks-Tonelli already. undo

21 December 2020

• curprev 22:1022:10, 21 December 2020 Tom.Reding talk contribs m 18,460 bytes +28 Enum 1 author/editor WL; WP:GenFixes on undo Tag: AWB

27 November 2020

• curprev 05:3505:35, 27 November 2020 Monkbot talk contribs m 18,432 bytes −7 Task 18 (cosmetic): eval 5 templates: del empty params (1×); undo Tag: AWB

28 July 2020

• curprev 06:4206:42, 28 July 2020 EmilJ talk contribs 18,439 bytes −20 →top: it's a square root "of" x, not "of" the modulus undo

15 April 2020

• curprev 05:2205:22, 15 April 2020 OAbot talk contribs m 18,459 bytes +17 Open access bot: doi added to citation with #oabot. undo

31 March 2020

• curprev 12:0312:03, 31 March 2020 2003:e5:bf19:4bc8:5802:3f39:483b:e8b8 talk 18,442 bytes −13 →The algorithm undo

20 March 2020

• curprev 20:2220:22, 20 March 2020 InternetArchiveBot talk contribs 18,455 bytes +73 Bluelink 1 book for verifiability (goog)) #IABot (v2.0) (GreenC bot undo

17 March 2020

• curprev 01:4601:46, 17 March 2020 Endo999 talk contribs 18,382 bytes +16 →Tonelli's algorithm will work on mod p^k: reference fixup undo

13 February 2020

• curprev 04:0904:09, 13 February 2020 GreenC bot talk contribs 18,366 bytes −23 Move 1 url. Wayback Medic 2.5 undo

3 January 2020

• curprev 07:5007:50, 3 January 2020 StefanoMaruelli talk contribs m 18,389 bytes +74 →References undo

19 November 2019

• curprev 09:5609:56, 19 November 2019 InternetArchiveBot talk contribs 18,315 bytes +147 Bluelink 1 book for verifiability.) #IABot (v2.0) (GreenC bot undo

10 June 2019

• curprev 02:1302:13, 10 June 2019 Endo999 talk contribs 18,168 bytes +30 →Tonelli's algorithm will work on mod p^k: lambda for y (closer to original terminology as per talk page suggestion) undo
• curprev 00:2100:21, 10 June 2019 Endo999 talk contribs 18,138 bytes +6 →Tonelli's algorithm will work on mod p^k: change of terminology noted by talk page undo

2 April 2019

• curprev 06:0006:00, 2 April 2019 71.187.248.147 talk 18,132 bytes −12 →The algorithm undo
• curprev 05:5905:59, 2 April 2019 71.187.248.147 talk 18,144 bytes −96 →The algorithm: It seems like someone tried to extend the applicability of this formula from primes to prime powers in an incorrect way. I have edited it so as to only include the prime case, which is correct. As the page says, there is a generalization to prime powers. But the algorithm described here is not that generalization. This article needs further edits in general. undo

2 March 2019

• curprev 23:4123:41, 2 March 2019 Davidfink314 talk contribs m 18,240 bytes +199 →clarified solution in p = 3 (mod 4) case undo

20 November 2018

• curprev 14:0914:09, 20 November 2018 141.134.36.157 talk 18,041 bytes −1 →Core ideas undo
• curprev 14:0814:08, 20 November 2018 141.134.36.157 talk 18,042 bytes +1 →Core ideas undo

18 September 2018

• curprev 12:5512:55, 18 September 2018 Magyar25 talk contribs m 18,041 bytes +59 No edit summary undo

14 June 2018

• curprev 12:4412:44, 14 June 2018 MwGamera talk contribs m 17,982 bytes −488 c/e undo

16 May 2018

• curprev 13:3413:34, 16 May 2018 OAbot talk contribs m 18,470 bytes +17 Open access bot: add arxiv identifier to citation with #oabot. undo

10 May 2018

• curprev 11:4411:44, 10 May 2018 PrimeHunter talk contribs 18,453 bytes +1 Undid revision 840514759 by 208.191.157.255 (talk). There are two "(", just not consecutive undo Tag: Undo
• curprev 11:3511:35, 10 May 2018 208.191.157.255 talk 18,452 bytes −1 →Speed of the algorithm: There was an extra ")" that I got rid of. undo

30 March 2018

• curprev 16:0016:00, 30 March 2018 Supersam654 talk contribs m 18,453 bytes 0 Proper grammar for specifying math variables in a sentence. undo

11 March 2018

• curprev 01:4601:46, 11 March 2018 GreenC bot talk contribs m 18,453 bytes −80 Reformat 2 archive links. Wayback Medic 2.1 undo

22 February 2018

• curprev 22:2722:27, 22 February 2018 PrimeHunter talk contribs 18,533 bytes +4 →Core ideas: link first occurrence of quadratic residue undo

21 February 2018

• curprev 05:2305:23, 21 February 2018 Endo999 talk contribs m 18,529 bytes +6 →Tonelli's algorithm will work on mod p^k undo
• curprev 05:2105:21, 21 February 2018 Endo999 talk contribs m 18,523 bytes +31 →Tonelli's algorithm will work on mod p^k undo
• curprev 05:1305:13, 21 February 2018 Endo999 talk contribs m 18,492 bytes +1 →Tonelli's algorithm will work on mod p^k undo
• curprev 05:0505:05, 21 February 2018 Endo999 talk contribs 18,491 bytes +3 →Tonelli's algorithm will work on mod p^k: reference fixup undo
• curprev 05:0405:04, 21 February 2018 Endo999 talk contribs m 18,488 bytes +2 →Tonelli's algorithm will work on mod p^k undo
• curprev 05:0305:03, 21 February 2018 Endo999 talk contribs m 18,486 bytes +1 →Tonelli's algorithm will work on mod p^k undo
• curprev 05:0205:02, 21 February 2018 Endo999 talk contribs 18,485 bytes +2,192 →Generalizations: dickson's theory of numbers shows Tonelli's algorithm can also do square roots mod p^k, not just mod p undo