Wilson's theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Wilson's theorem" in English language version.

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Cosgrave, John B.; Dilcher, Karl (2008). "Extensions of the Gauss–Wilson theorem". Integers. 8 A39. MR 2472057.

archive.org

Giovanni Vacca (1899) "Sui manoscritti inediti di Leibniz" (On unpublished manuscripts of Leibniz), Bollettino di bibliografia e storia delle scienze matematiche ... (Bulletin of the bibliography and history of mathematics), vol. 2, pages 113–116; see page 114 (in Italian). Vacca quotes from Leibniz's mathematical manuscripts kept at the Royal Public Library in Hanover (Germany), vol. 3 B, bundle 11, page 10:
Original : Inoltre egli intravide anche il teorema di Wilson, come risulta dall'enunciato seguente:
"Productus continuorum usque ad numerum qui antepraecedit datum divisus per datum relinquit 1 (vel complementum ad unum?) si datus sit primitivus. Si datus sit derivativus relinquet numerum qui cum dato habeat communem mensuram unitate majorem."
Egli non giunse pero a dimostrarlo.
Translation : In addition, he [Leibniz] also glimpsed Wilson's theorem, as shown in the following statement:
"The product of all integers preceding the given integer, when divided by the given integer, leaves 1 (or the complement of 1?) if the given integer be prime. If the given integer be composite, it leaves a number which has a common factor with the given integer [which is] greater than one."
However, he didn't succeed in proving it.
See also: Giuseppe Peano, ed., Formulaire de mathématiques, vol. 2, no. 3, page 85 (1897).
Landau, Edmund (1966) [1927]. "Part One, Chapter V: Congruences, Theorem 77". Elementary Number Theory (2nd ed.). New York: Chelsea Publishing Company. pp. 51–52. LCCN 66002147. OCLC 1420155. OL 5976039M. Retrieved 2025-02-06.

books.google.com

Edward Waring, Meditationes Algebraicae (Cambridge, England: 1770), page 218 (in Latin). In the third (1782) edition of Waring's Meditationes Algebraicae, Wilson's theorem appears as problem 5 on page 380. On that page, Waring states: "Hanc maxime elegantem primorum numerorum proprietatem invenit vir clarissimus, rerumque mathematicarum peritissimus Joannes Wilson Armiger." (A man most illustrious and most skilled in mathematics, Squire John Wilson, found this most elegant property of prime numbers.)
Joseph Louis Lagrange, "Demonstration d'un théorème nouveau concernant les nombres premiers" (Proof of a new theorem concerning prime numbers), Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres (Berlin), vol. 2, pages 125–137 (1771).
Giovanni Vacca (1899) "Sui manoscritti inediti di Leibniz" (On unpublished manuscripts of Leibniz), Bollettino di bibliografia e storia delle scienze matematiche ... (Bulletin of the bibliography and history of mathematics), vol. 2, pages 113–116; see page 114 (in Italian). Vacca quotes from Leibniz's mathematical manuscripts kept at the Royal Public Library in Hanover (Germany), vol. 3 B, bundle 11, page 10:
Original : Inoltre egli intravide anche il teorema di Wilson, come risulta dall'enunciato seguente:
"Productus continuorum usque ad numerum qui antepraecedit datum divisus per datum relinquit 1 (vel complementum ad unum?) si datus sit primitivus. Si datus sit derivativus relinquet numerum qui cum dato habeat communem mensuram unitate majorem."
Egli non giunse pero a dimostrarlo.
Translation : In addition, he [Leibniz] also glimpsed Wilson's theorem, as shown in the following statement:
"The product of all integers preceding the given integer, when divided by the given integer, leaves 1 (or the complement of 1?) if the given integer be prime. If the given integer be composite, it leaves a number which has a common factor with the given integer [which is] greater than one."
However, he didn't succeed in proving it.
See also: Giuseppe Peano, ed., Formulaire de mathématiques, vol. 2, no. 3, page 85 (1897).

emis.de

Cosgrave, John B.; Dilcher, Karl (2008). "Extensions of the Gauss–Wilson theorem". Integers. 8 A39. MR 2472057.

loc.gov

lccn.loc.gov

Landau, Edmund (1966) [1927]. "Part One, Chapter V: Congruences, Theorem 77". Elementary Number Theory (2nd ed.). New York: Chelsea Publishing Company. pp. 51–52. LCCN 66002147. OCLC 1420155. OL 5976039M. Retrieved 2025-02-06.

openlibrary.org

Landau, Edmund (1966) [1927]. "Part One, Chapter V: Congruences, Theorem 77". Elementary Number Theory (2nd ed.). New York: Chelsea Publishing Company. pp. 51–52. LCCN 66002147. OCLC 1420155. OL 5976039M. Retrieved 2025-02-06.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F. "Abu Ali al-Hasan ibn al-Haytham". MacTutor History of Mathematics Archive. University of St Andrews.

worldcat.org

search.worldcat.org

Landau, Edmund (1966) [1927]. "Part One, Chapter V: Congruences, Theorem 77". Elementary Number Theory (2nd ed.). New York: Chelsea Publishing Company. pp. 51–52. LCCN 66002147. OCLC 1420155. OL 5976039M. Retrieved 2025-02-06.