@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-NM1F1MRK-M
  skos:prefLabel "modular arithmetic"@en, "arithmétique modulaire"@fr ;
  a skos:Concept ;
  skos:narrower psr:-VZ14L1BC-W .

psr:-VZ14L1BC-W
  skos:prefLabel "congruence de carrés"@fr, "congruence of squares"@en ;
  skos:broader psr:-PQ16LFVV-N, psr:-NM1F1MRK-M ;
  skos:definition """En arithmétique modulaire, une <b>congruence de carrés</b> modulo un entier naturel <i>n</i> est une équation de la forme  <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 x^{2}\\\\equiv y^{2}{\\\\pmod {n}}\\\\qquad {\\\\hbox{avec}}\\\\qquad x\\
ot \\\\equiv \\\\pm y{\\\\pmod {n}}.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>≡<!-- ≡ --></mo>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <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>         <mspace width="2em"></mspace>         <mrow class="MJX-TeXAtom-ORD">           <mstyle displaystyle="false" scriptlevel="0">             <mtext>avec</mtext>           </mstyle>         </mrow>         <mspace width="2em"></mspace>         <mi>x</mi>         <mo>≢</mo>         <mo>±<!-- ± --></mo>         <mi>y</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 x^{2}\\\\equiv y^{2}{\\\\pmod {n}}\\\\qquad {\\\\hbox{avec}}\\\\qquad x\\
ot \\\\equiv \\\\pm y{\\\\pmod {n}}.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57b5a2cca8002e9dd69ce5a469a4e6e4aab96b89" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:51.639ex; height:3.176ex;" alt="{\\\\displaystyle x^{2}\\\\equiv y^{2}{\\\\pmod {n}}\\\\qquad {\\\\hbox{avec}}\\\\qquad x\\
ot \\\\equiv \\\\pm y{\\\\pmod {n}}.}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Congruence_de_carr%C3%A9s">https://fr.wikipedia.org/wiki/Congruence_de_carr%C3%A9s</a>)"""@fr, """In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Congruence_of_squares">https://en.wikipedia.org/wiki/Congruence_of_squares</a>)"""@en ;
  dc:created "2023-08-28"^^xsd:date ;
  skos:inScheme psr: ;
  skos:related psr:-LRPB5V08-Q ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Congruence_of_squares>, <https://fr.wikipedia.org/wiki/Congruence_de_carr%C3%A9s> ;
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept .

psr: a skos:ConceptScheme .
psr:-PQ16LFVV-N
  skos:prefLabel "factorization"@en, "factorisation"@fr ;
  a skos:Concept ;
  skos:narrower psr:-VZ14L1BC-W .

psr:-LRPB5V08-Q
  skos:prefLabel "square number"@en, "nombre carré"@fr ;
  a skos:Concept ;
  skos:related psr:-VZ14L1BC-W .