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- Eulers_totient_function abstract "In number theory, Euler's totient function (or Euler's phi function), denoted as φ(n) or ϕ(n), is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n. (These integers are sometimes referred to as totatives of 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 the greatest common divisor gcd(n, k) = 1.Euler's totient function is a multiplicative function, meaning that if two numbers m and n are coprime, 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.Euler's phi function is important mainly because it gives the order of the multiplicative group of integers modulo n (the group of units of the ring ℤ/nℤ). It also plays a key role in the definition of the RSA encryption system.".
- Eulers_totient_function thumbnail EulerPhi.svg?width=300.
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- Eulers_totient_function wikiPageWikiLink An_Introduction_to_the_Theory_of_Numbers.
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- Eulers_totient_function wikiPageWikiLink Annals_of_Mathematics.
- Eulers_totient_function wikiPageWikiLink Arithmetic_function.
- Eulers_totient_function wikiPageWikiLink Arnold_Walfisz.
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- Eulers_totient_function wikiPageWikiLink Carmichaels_totient_function_conjecture.
- Eulers_totient_function wikiPageWikiLink Category:Algebra.
- Eulers_totient_function wikiPageWikiLink Category:Articles_containing_proofs.
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- Eulers_totient_function wikiPageWikiLink Category:Multiplicative_functions.
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- Eulers_totient_function wikiPageWikiLink Euler–Mascheroni_constant.
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- Eulers_totient_function wikiPageWikiLink Integer_factorization.
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- Eulers_totient_function wikiPageWikiLink Jordans_totient_function.
- Eulers_totient_function wikiPageWikiLink Lagranges_theorem_(group_theory).
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- Eulers_totient_function wikiPageWikiLink Möbius_function.
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- Eulers_totient_function wikiPageWikiLink Prime_number.
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- Eulers_totient_function wikiPageWikiLink RSA_(cryptosystem).
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- Eulers_totient_function wikiPageWikiLink Riemann_hypothesis.
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- Eulers_totient_function wikiPageWikiLink Ring_(mathematics).
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- Eulers_totient_function wikiPageWikiLink File:EulerPhi.svg.
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- Eulers_totient_function wikiPageWikiLinkText "φ function".
- Eulers_totient_function wikiPageWikiLinkText "φ".
- Eulers_totient_function wikiPageWikiLinkText "φ(n)".
- Eulers_totient_function wikiPageWikiLinkText "''φ''".
- Eulers_totient_function wikiPageWikiLinkText "Euler phi-function".
- Eulers_totient_function wikiPageWikiLinkText "Euler φ-function".
- Eulers_totient_function wikiPageWikiLinkText "Euler's totient function".