@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-Q3G3SRHB-H
  skos:definition """La congruence sur les entiers est une relation pouvant unir deux entiers. Elle fut pour la première fois étudiée en tant que structure par le mathématicien allemand Carl Friedrich Gauss à la fin du XVIIIe siècle et présentée au public dans ses Disquisitiones arithmeticae en 1801. Elle est aujourd'hui couramment utilisée en théorie des nombres, en algèbre générale et en cryptographie. Elle représente le fondement d'une branche mathématique appelée arithmétique modulaire. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Congruence_sur_les_entiers">https://fr.wikipedia.org/wiki/Congruence_sur_les_entiers</a>)"""@fr, """Given an integer <span class="texhtml"><i>n</i> > 1</span>, called a <b>modulus</b>, two integers <span class="texhtml mvar" style="font-style:italic;">a</span> and <span class="texhtml mvar" style="font-style:italic;">b</span> are said to be <b>congruent</b> modulo <span class="texhtml mvar" style="font-style:italic;">n</span>, if <span class="texhtml mvar" style="font-style:italic;">n</span> is a divisor of their difference: that is, if there is an integer <span class="texhtml"><i>k</i></span> such that: <blockquote><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a-b=kn.}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>a</mi>
         <mo>−<!-- − --></mo>
         <mi>b</mi>
         <mo>=</mo>
         <mi>k</mi>
         <mi>n</mi>
         <mo>.</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle a-b=kn.}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50b2450f955571e582908a54d114199252d38cf0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.419ex; height:2.343ex;" alt="{\\\\displaystyle a-b=kn.}"></span></blockquote>Congruence modulo <span class="texhtml mvar" style="font-style:italic;">n</span> is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo <span class="texhtml mvar" style="font-style:italic;">n</span> is denoted:
         <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a\\\\equiv b{\\\\pmod {n}}.}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>a</mi>
         <mo>≡<!-- ≡ --></mo>
         <mi>b</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mspace width="1em"></mspace>
         <mo stretchy="false">(</mo>
         <mi>mod</mi>
         <mspace width="0.333em"></mspace>
         <mi>n</mi>
         <mo stretchy="false">)</mo>
         </mrow>
         <mo>.</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle a\\\\equiv b{\\\\pmod {n}}.}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5cfa7bf9486797d6337650b0bdfb4810484c35a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.051ex; height:2.843ex;" alt="{\\\\displaystyle a\\\\equiv b{\\\\pmod {n}}.}"></span></dd></dl>
         The parentheses mean that <span class="texhtml">(mod <i>n</i>)</span> applies to the entire equation, not just to the right-hand side (here, <span class="texhtml mvar" style="font-style:italic;">b</span>). 
         
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Modular_arithmetic#Congruence">https://en.wikipedia.org/wiki/Modular_arithmetic#Congruence</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-F7SFNL4R-1 ;
  skos:prefLabel "congruence sur les entiers"@fr, "congruence"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Congruence_sur_les_entiers>, <https://en.wikipedia.org/wiki/Modular_arithmetic#Congruence> .

psr: a skos:ConceptScheme .
psr:-F7SFNL4R-1
  skos:prefLabel "algebraic number theory"@en, "théorie algébrique des nombres"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q3G3SRHB-H .