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Fungrim entry: 081abd

φ ⁣(2n)=2n−1\varphi\!\left({2}^{n}\right) = {2}^{n - 1}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\varphi\!\left({2}^{n}\right) = {2}^{n - 1}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("081abd"),
    Formula(Equal(Totient(Pow(2, n)), Pow(2, Sub(n, 1)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC