PlanetMath: Euler-Fermat theorem

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Euler-Fermat theorem

(Theorem)

If $a,n \in \mathbb{Z}$ such that $\gcd(a,n)=1$ , then $a^{\varphi (n)} \equiv 1 \operatorname{mod} n$ , where $\varphi$ is the Euler totient function.

"Euler-Fermat theorem" is owned by Wkbj79. [ full author list (2) | owner history (1) ]

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Other names:

Euler's theorem

Keywords:

number theory

Attachments:: proof of Euler-Fermat theorem (Proof) by KimJ
corollary of Euler-Fermat theorem (Result) by kamala
proof of Euler-Fermat theorem using Lagrange's theorem (Proof) by alozano

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Cross-references: Euler totient function
There are 6 references to this entry.

This is version 6 of Euler-Fermat theorem, born on 2001-10-15, modified 2007-08-23.
Object id is 198, canonical name is EulerFermatTheorem.
Accessed 18376 times total.

Classification:

AMS MSC:	11-00 (Number theory :: General reference works )
	20-01 (Group theory and generalizations :: Instructional exposition )
	20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties)

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