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Fungrim entry: c19cd6

φ(n)=#{k:k{1,2,,n}andgcd ⁣(n,k)=1}\varphi(n) = \# \left\{ k : k \in \{1, 2, \ldots, n\} \,\mathbin{\operatorname{and}}\, \gcd\!\left(n, k\right) = 1 \right\}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\varphi(n) = \# \left\{ k : k \in \{1, 2, \ldots, n\} \,\mathbin{\operatorname{and}}\, \gcd\!\left(n, k\right) = 1 \right\}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
Cardinality#S\# S Set cardinality
Range{a,a+1,,b}\{a, a + 1, \ldots, b\} Integers between given endpoints
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("c19cd6"),
    Formula(Equal(Totient(n), Cardinality(Set(k, For(k), And(Element(k, Range(1, n)), Equal(GCD(n, k), 1)))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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2020-01-31 18:09:28.494564 UTC