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dbpedia-owl:abstract
  • Dalam teori bilangan, teorema Euler (juga dikenal sebagai teorema Fermat-Euler) menyatakan bahwa jika n adalah bilangan bulat positif, dan a adalah prima relatif dengan n, maka aφ(n) = 1 (mod n)di mana φ(n) melambangkan fungsi phi Euler.
  • Twierdzenie Eulera o liczbach względnie pierwszych to twierdzenie teorii liczb, które mówi, co następuje:
  • Devido à numerosa produção teórica de Leonhard Euler, a expressão Teorema de Euler pode ser aplicada a um grande número de teoremas matemáticos e físicos: O Teorema do Deslocamento de Euler, ou Teorema da Rotação de Euler, em Mecânica dos Corpos Rígidos O Teorema da Distribuição de Euler, em Geometria O Teorema do Tociente, ou Teorema de Fermat-Euler, em Teoria dos Números O Teorema de Euler em Trigonometria O Teorema de Euler sobre as Diferenciais Exatas, em Cálculo
  • 数論において、オイラーの定理(Euler's theorem)は初等整数論の最も基本的な定理の一つである。
  • Az Euler–Fermat-tétel a számelmélet egyik nagyon fontos állítása.
  • In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, thenwhere φ(n) is Euler's totient function. (The notation is explained in the article Modular arithmetic.) In 1736, Euler published his proof of Fermat's little theorem, which Fermat had presented without proof. Subsequently, Euler presented other proofs of the theorem, culminating with "Euler's theorem" in his paper of 1763, in which he attempted to find the smallest exponent for which Fermat's little theorem was always true.There is a converse of Euler's theorem: if the above congruence is true, then a and n must be coprime.The theorem is a generalization of Fermat's little theorem, and is further generalized by Carmichael's theorem.The theorem may be used to easily reduce large powers modulo n. For example, consider finding the ones place decimal digit of 7222, i.e. 7222 (mod 10). Note that 7 and 10 are coprime, and φ(10) = 4. So Euler's theorem yields 74 ≡ 1 (mod 10), and we get 7222 ≡ 74 × 55 + 2 ≡ (74)55 × 72 ≡ 155 × 72 ≡ 49 ≡ 9 (mod 10).In general, when reducing a power of a modulo n (where a and n are coprime), one needs to work modulo φ(n) in the exponent of a:if x ≡ y (mod φ(n)), then ax ≡ ay (mod n).Euler's theorem also forms the basis of the RSA encryption system: encryption and decryption in this system together amount to exponentiating the original text by kφ(n) + 1 for some positive integer k, so Euler's theorem shows that the decrypted result is the same as the original.
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rdfs:comment
  • Dalam teori bilangan, teorema Euler (juga dikenal sebagai teorema Fermat-Euler) menyatakan bahwa jika n adalah bilangan bulat positif, dan a adalah prima relatif dengan n, maka aφ(n) = 1 (mod n)di mana φ(n) melambangkan fungsi phi Euler.
  • Twierdzenie Eulera o liczbach względnie pierwszych to twierdzenie teorii liczb, które mówi, co następuje:
  • Devido à numerosa produção teórica de Leonhard Euler, a expressão Teorema de Euler pode ser aplicada a um grande número de teoremas matemáticos e físicos: O Teorema do Deslocamento de Euler, ou Teorema da Rotação de Euler, em Mecânica dos Corpos Rígidos O Teorema da Distribuição de Euler, em Geometria O Teorema do Tociente, ou Teorema de Fermat-Euler, em Teoria dos Números O Teorema de Euler em Trigonometria O Teorema de Euler sobre as Diferenciais Exatas, em Cálculo
  • 数論において、オイラーの定理(Euler's theorem)は初等整数論の最も基本的な定理の一つである。
  • Az Euler–Fermat-tétel a számelmélet egyik nagyon fontos állítása.
  • In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, thenwhere φ(n) is Euler's totient function. (The notation is explained in the article Modular arithmetic.) In 1736, Euler published his proof of Fermat's little theorem, which Fermat had presented without proof.
rdfs:label
  • Théorème d'Euler (arithmétique)
  • Теорема Эйлера (теория чисел)
  • Euler teoremi
  • Euler's theorem
  • Eulerova věta (teorie čísel)
  • Euler–Fermat-tétel
  • Satz von Euler
  • Stelling van Euler
  • Teorema Euler
  • Teorema d'Euler
  • Teorema de Euler
  • Teorema de Euler
  • Teorema di Eulero (aritmetica modulare)
  • Twierdzenie Eulera (teoria liczb)
  • Теорема на Ойлер
  • オイラーの定理 (数論)
  • 오일러의 정리
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