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- Euler's_totient_function abstract "In number theory, Euler's totient or phi function, φ(n), is an arithmetic function that counts the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Thus if n is a positive integer, then φ(n) is the number of integers k in the range 1 ≤ k ≤ n for which gcd(n, k) = 1. The totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime (to each other), then φ(mn) = φ(m)φ(n).For example let n = 9. Then gcd(9, 3) = gcd(9, 6) = 3 and gcd(9, 9) = 9. The other six numbers in the range 1 ≤ k ≤ 9, that is, 1, 2, 4, 5, 7 and 8, are relatively prime to 9. Therefore, φ(9) = 6. As another example, φ(1) = 1 since gcd(1, 1) = 1.The totient function is important mainly because it gives the order of the multiplicative group of integers modulo n (the group of units of the ring ). See Euler's theorem. The totient function also plays a key role in the definition of the RSA encryption system.".
- Euler's_totient_function thumbnail EulerPhi.svg?width=300.
- Euler's_totient_function wikiPageExternalLink 1211.2025.pdf.
- Euler's_totient_function wikiPageExternalLink cmj034-042.pdf.
- Euler's_totient_function wikiPageExternalLink bd50b5ae25c74465.
- Euler's_totient_function wikiPageExternalLink vol8.html.
- Euler's_totient_function wikiPageExternalLink eulertotientfunction.htm.
- Euler's_totient_function wikiPageExternalLink read.php?5,359275,359275.
- Euler's_totient_function wikiPageExternalLink rdineva1.pdf.
- Euler's_totient_function wikiPageExternalLink mathconf-0.pdf.
- Euler's_totient_function wikiPageID "53452".
- Euler's_totient_function wikiPageRevisionID "605482653".
- Euler's_totient_function hasPhotoCollection Euler's_totient_function.
- Euler's_totient_function id "p/t110040".
- Euler's_totient_function title "Totient function".
- Euler's_totient_function subject Category:Articles_containing_proofs.
- Euler's_totient_function subject Category:Modular_arithmetic.
- Euler's_totient_function subject Category:Multiplicative_functions.
- Euler's_totient_function subject Category:Number_theory.
- Euler's_totient_function type Abstraction100002137.
- Euler's_totient_function type Function113783816.
- Euler's_totient_function type MathematicalRelation113783581.
- Euler's_totient_function type MultiplicativeFunctions.
- Euler's_totient_function type Relation100031921.
- Euler's_totient_function comment "In number theory, Euler's totient or phi function, φ(n), is an arithmetic function that counts the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Thus if n is a positive integer, then φ(n) is the number of integers k in the range 1 ≤ k ≤ n for which gcd(n, k) = 1. The totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime (to each other), then φ(mn) = φ(m)φ(n).For example let n = 9.".
- Euler's_totient_function label "Euler's totient function".
- Euler's_totient_function label "Eulersche Phi-Funktion".
- Euler's_totient_function label "Función φ de Euler".
- Euler's_totient_function label "Funkcja φ".
- Euler's_totient_function label "Funzione φ di Eulero".
- Euler's_totient_function label "Função totiente de Euler".
- Euler's_totient_function label "Indicator (getaltheorie)".
- Euler's_totient_function label "Indicatrice d'Euler".
- Euler's_totient_function label "Функция Эйлера".
- Euler's_totient_function label "مؤشر أويلر".
- Euler's_totient_function label "オイラーのφ関数".
- Euler's_totient_function label "欧拉函数".
- Euler's_totient_function sameAs Eulerova_funkce.
- Euler's_totient_function sameAs Eulersche_Phi-Funktion.
- Euler's_totient_function sameAs Συνάρτηση_Όιλερ.
- Euler's_totient_function sameAs Función_φ_de_Euler.
- Euler's_totient_function sameAs Indicatrice_d'Euler.
- Euler's_totient_function sameAs Funzione_φ_di_Eulero.
- Euler's_totient_function sameAs オイラーのφ関数.
- Euler's_totient_function sameAs 오일러_피_함수.
- Euler's_totient_function sameAs Indicator_(getaltheorie).
- Euler's_totient_function sameAs Funkcja_φ.
- Euler's_totient_function sameAs Função_totiente_de_Euler.
- Euler's_totient_function sameAs m.0f063.
- Euler's_totient_function sameAs Q190026.
- Euler's_totient_function sameAs Q190026.
- Euler's_totient_function sameAs Euler's_totient_function.
- Euler's_totient_function wasDerivedFrom Euler's_totient_function?oldid=605482653.
- Euler's_totient_function depiction EulerPhi.svg.
- Euler's_totient_function isPrimaryTopicOf Euler's_totient_function.