# Fungrim entry: 7b27cd

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

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Cardinality$\# S$ Set cardinality
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Totient$\varphi(n)$ Euler totient function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("7b27cd"),
Formula(Equal(Cardinality(Set(k, For(k), And(Element(k, Range(1, n)), Equal(GCD(n, k), 1)))), Totient(n))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(1))))

## Topics using this entry

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