Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Fermat's_theorem_on_sums_of_two_squares> ?p ?o. }
Showing items 1 to 37 of
37
with 100 items per page.
- Fermat's_theorem_on_sums_of_two_squares abstract "In additive number theory, Pierre de Fermat's theorem on sums of two squares states that an odd prime p is expressible aswith x and y integers, if and only ifFor example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways:On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares.Albert Girard was the first to make the observation (in 1632) and Fermat was first to claim a proof of it.Fermat announced this theorem in a letter to Marin Mersenne dated December 25, 1640; for this reason this theorem is sometimes called Fermat's Christmas Theorem.Since the Brahmagupta–Fibonacci identity implies that the product of two integers that can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer n, we see that if all of n's odd prime factors congruent to 3 modulo 4 occur to an even exponent, it is expressible as a sum of two squares. The converse also holds.".
- Fermat's_theorem_on_sums_of_two_squares wikiPageID "1850216".
- Fermat's_theorem_on_sums_of_two_squares wikiPageRevisionID "601121514".
- Fermat's_theorem_on_sums_of_two_squares hasPhotoCollection Fermat's_theorem_on_sums_of_two_squares.
- Fermat's_theorem_on_sums_of_two_squares subject Category:Additive_number_theory.
- Fermat's_theorem_on_sums_of_two_squares subject Category:Theorems_in_number_theory.
- Fermat's_theorem_on_sums_of_two_squares type Abstraction100002137.
- Fermat's_theorem_on_sums_of_two_squares type Communication100033020.
- Fermat's_theorem_on_sums_of_two_squares type Message106598915.
- Fermat's_theorem_on_sums_of_two_squares type Proposition106750804.
- Fermat's_theorem_on_sums_of_two_squares type Statement106722453.
- Fermat's_theorem_on_sums_of_two_squares type Theorem106752293.
- Fermat's_theorem_on_sums_of_two_squares type TheoremsInNumberTheory.
- Fermat's_theorem_on_sums_of_two_squares comment "In additive number theory, Pierre de Fermat's theorem on sums of two squares states that an odd prime p is expressible aswith x and y integers, if and only ifFor example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways:On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares.Albert Girard was the first to make the observation (in 1632) and Fermat was first to claim a proof of it.Fermat announced this theorem in a letter to Marin Mersenne dated December 25, 1640; for this reason this theorem is sometimes called Fermat's Christmas Theorem.Since the Brahmagupta–Fibonacci identity implies that the product of two integers that can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer n, we see that if all of n's odd prime factors congruent to 3 modulo 4 occur to an even exponent, it is expressible as a sum of two squares. ".
- Fermat's_theorem_on_sums_of_two_squares label "Fermat's theorem on sums of two squares".
- Fermat's_theorem_on_sums_of_two_squares label "Stelling van Fermat over de som van twee kwadraten".
- Fermat's_theorem_on_sums_of_two_squares label "Teorema de Fermat sobre la suma de dos cuadrados".
- Fermat's_theorem_on_sums_of_two_squares label "Teorema di Fermat sulle somme di due quadrati".
- Fermat's_theorem_on_sums_of_two_squares label "Théorème des deux carrés de Fermat".
- Fermat's_theorem_on_sums_of_two_squares label "Twierdzenie Fermata o sumie dwóch kwadratów".
- Fermat's_theorem_on_sums_of_two_squares label "Теорема Ферма — Эйлера".
- Fermat's_theorem_on_sums_of_two_squares label "مبرهنة فيرما حول مجموع مربعين".
- Fermat's_theorem_on_sums_of_two_squares label "二個の平方数の和".
- Fermat's_theorem_on_sums_of_two_squares label "费马平方和定理".
- Fermat's_theorem_on_sums_of_two_squares sameAs Teorema_de_Fermat_sobre_la_suma_de_dos_cuadrados.
- Fermat's_theorem_on_sums_of_two_squares sameAs Théorème_des_deux_carrés_de_Fermat.
- Fermat's_theorem_on_sums_of_two_squares sameAs Teorema_di_Fermat_sulle_somme_di_due_quadrati.
- Fermat's_theorem_on_sums_of_two_squares sameAs 二個の平方数の和.
- Fermat's_theorem_on_sums_of_two_squares sameAs 페르마의_두_제곱수_정리.
- Fermat's_theorem_on_sums_of_two_squares sameAs Stelling_van_Fermat_over_de_som_van_twee_kwadraten.
- Fermat's_theorem_on_sums_of_two_squares sameAs Twierdzenie_Fermata_o_sumie_dwóch_kwadratów.
- Fermat's_theorem_on_sums_of_two_squares sameAs m.060xk9.
- Fermat's_theorem_on_sums_of_two_squares sameAs Q914517.
- Fermat's_theorem_on_sums_of_two_squares sameAs Q914517.
- Fermat's_theorem_on_sums_of_two_squares sameAs Fermat's_theorem_on_sums_of_two_squares.
- Fermat's_theorem_on_sums_of_two_squares wasDerivedFrom Fermat's_theorem_on_sums_of_two_squares?oldid=601121514.
- Fermat's_theorem_on_sums_of_two_squares isPrimaryTopicOf Fermat's_theorem_on_sums_of_two_squares.