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Fungrim entry: b81b45

(nP)    (φ ⁣(n)nn)\left(n \notin \mathbb{P}\right) \implies \left(\varphi\!\left(n\right) \le n - \sqrt{n}\right)
Assumptions:nZ2n \in \mathbb{Z}_{\ge 2}
TeX:
\left(n \notin \mathbb{P}\right) \implies \left(\varphi\!\left(n\right) \le n - \sqrt{n}\right)

n \in \mathbb{Z}_{\ge 2}
Definitions:
Fungrim symbol Notation Short description
PPP\mathbb{P} Prime numbers
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Sqrtz\sqrt{z} Principal square root
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("b81b45"),
    Formula(Implies(NotElement(n, PP), LessEqual(Totient(n), Sub(n, Sqrt(n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(2))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC