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Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle n} that are relatively prime to n {\displaystyle n} . It is written using the Greek letter phi as φ ( n ) {\displaystyle \varphi (n)} or ϕ ( n ) {\displaystyle \phi (n)} , and may also be called Euler's phi function. In other words, it is the…

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Overview

History, terminology, and notation

Computing Euler's totient function

Some values

Euler's theorem

Other formulae

Generating functions

Growth rate

Ratio of consecutive values

Totient number

Applications

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Euler's totient function

Nodes87
Edges86
Triples37
Avg. degree1.98
Density0.022989
Components1

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Euler's totient function

Top relations

related to External links · 17
Euler's totient function → Archived, Chinese Remainder Theorem, Divisor Functions Archived, EMS Press, Encyclopedia, Euler Phi Function, Euler's Phi Function, JavaScript, Loomis, Mathematics, Möbius, Polhill Summing Up The, Rosica, The Euler Totient, Totient, Wayback MachineEuler's, Wayback MachinePlytage
related to history · 14
Euler's totient function → Disquisitiones Arithmeticae, Euler, Euler's, Gauss, Gauss's, Greek, However, In, Jordan's, Leonhard Euler, Sylvester, The, This, Thus
related to Totient number · 5
Euler's totient function → A002202, Euler's, Every, The, There
is a · 1
Euler's totient function → multiplicative function

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Important terminology

displaystyle prime function number numbers varphi totient euler's gcd integers formula integer positive also multiplicative 20 sum theorem proof relatively

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Euler's totient functionis amultiplicative function0.90text
Euler's totient functionrelated to External linksTotient0.60section
Euler's totient functionrelated to External linksEncyclopedia0.60section
Euler's totient functionrelated to External linksMathematics0.60section
Euler's totient functionrelated to External linksEMS Press0.60section
Euler's totient functionrelated to External linksEuler's Phi Function0.60section
Euler's totient functionrelated to External linksChinese Remainder Theorem0.60section
Euler's totient functionrelated to External linksArchived0.60section
Euler's totient functionrelated to External linksWayback MachineEuler's0.60section
Euler's totient functionrelated to External linksJavaScript0.60section
Euler's totient functionrelated to External linksRosica0.60section
Euler's totient functionrelated to External linksThe Euler Totient0.60section

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