Fungrim home page

Fungrim entry: a68214

aφ(n)1(modn){a}^{\varphi(n)} \equiv 1 \pmod {n}
Assumptions:aZandnZ1andgcd ⁣(a,n)=1a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \gcd\!\left(a, n\right) = 1
TeX:
{a}^{\varphi(n)} \equiv 1 \pmod {n}

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \gcd\!\left(a, n\right) = 1
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Totientφ(n)\varphi(n) Euler totient function
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Source code for this entry:
Entry(ID("a68214"),
    Formula(CongruentMod(Pow(a, Totient(n)), 1, n)),
    Variables(a, n),
    Assumptions(And(Element(a, ZZ), Element(n, ZZGreaterEqual(1)), Equal(GCD(a, n), 1))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC