<?xml version="1.0" encoding="UTF-8"?>

<record version="6" id="198">
 <title>Euler-Fermat theorem</title>
 <name>EulerFermatTheorem</name>
 <created>2001-10-15 19:15:05</created>
 <modified>2007-08-23 21:29:40</modified>
 <type>Theorem</type>
 <creator id="1863" name="Wkbj79"/>
 <author id="1863" name="Wkbj79"/>
 <author id="5" name="KimJ"/>
 <classification>
	<category scheme="msc" code="11-00"/>
	<category scheme="msc" code="20-01"/>
	<category scheme="msc" code="20A05"/>
 </classification>
 <synonyms>
	<synonym concept="Euler-Fermat theorem" alias="Euler's theorem"/>
 </synonyms>
 <related>
	<object name="FermatsLittleTheorem"/>
	<object name="FermatsTheoremProof"/>
 </related>
 <keywords>
	<term>number theory</term>
 </keywords>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
</preamble>
 <content>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.</content>
</record>
