Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
arithmetic function
|
| gptkbp:alsoKnownAs |
gptkb:Euler's_totient_function
phi function |
| gptkbp:application |
gptkb:RSA_cryptosystem
gptkb:Euler's_theorem number theory |
| gptkbp:codomain |
non-negative integers
|
| gptkbp:defines |
number of positive integers less than or equal to n that are coprime to n
|
| gptkbp:designer |
no simple closed form
|
| gptkbp:domain |
positive integers
|
| gptkbp:form |
φ(n) = n × Π(1 - 1/p) over all distinct prime divisors p of n
|
| gptkbp:hasSpecialCase |
φ(1) = 1
φ(p) = p-1 for prime p |
| https://www.w3.org/2000/01/rdf-schema#label |
Euler totient function φ(n)
|
| gptkbp:introduced |
gptkb:Leonhard_Euler
|
| gptkbp:introducedIn |
1763
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:notation |
φ(n)
phi(n) |
| gptkbp:property |
sum of φ(d) over all divisors d of n equals n
φ(mn) = φ(m)φ(n) if gcd(m, n) = 1 multiplicative function average order is 6n/π² |
| gptkbp:relatedTo |
gptkb:Carmichael_function
gptkb:Möbius_function prime numbers |
| gptkbp:sequence |
gptkb:A000010_(OEIS)
|
| gptkbp:usedIn |
cryptography
group theory modular arithmetic |
| gptkbp:bfsParent |
gptkb:A002322
|
| gptkbp:bfsLayer |
8
|