Fungrim entry: b81b45

\left(n \notin \mathbb{P}\right) \;\implies\; \left(\varphi(n) \le n - \sqrt{n}\right)

Assumptions:

n \in \mathbb{Z}_{\ge 2}

TeX:

\left(n \notin \mathbb{P}\right) \;\implies\; \left(\varphi(n) \le n - \sqrt{n}\right)

n \in \mathbb{Z}_{\ge 2}

Definitions:

Fungrim symbol	Notation	Short description
`PP`	$\mathbb{P}$	Prime numbers
`Totient`	$\varphi(n)$	Euler totient function
`Sqrt`	$\sqrt{z}$	Principal square root
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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))))

Topics using this entry

Totient function

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

2021-03-15 19:12:00.328586 UTC