@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:-W90JFV07-V
  skos:prefLabel "multiplicative function"@en, "fonction multiplicative"@fr ;
  a skos:Concept ;
  skos:narrower psr:-PD794NH6-5 .

psr: a skos:ConceptScheme .
psr:-PD794NH6-5
  skos:exactMatch <https://fr.wikipedia.org/wiki/Indicatrice_d%27Euler>, <https://en.wikipedia.org/wiki/Euler%27s_totient_function> ;
  a skos:Concept ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:inScheme psr: ;
  skos:prefLabel "Euler's totient function"@en, "indicatrice d'Euler"@fr ;
  skos:definition """In number theory, <b>Euler's totient function</b> counts the positive integers up to a given integer <span class="texhtml mvar" style="font-style:italic;">n</span> that are relatively prime to <span class="texhtml mvar" style="font-style:italic;">n</span>. It is written using the Greek letter phi as <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 \\\\varphi (n)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>φ<!-- φ --></mi>         <mo stretchy="false">(</mo>         <mi>n</mi>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\varphi (n)}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f067864064667dd5f8b2508b9cbf983d89788629" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.724ex; height:2.843ex;" alt="{\\\\displaystyle \\\\varphi (n)}"></span> or <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 \\\\phi (n)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>ϕ<!-- ϕ --></mi>         <mo stretchy="false">(</mo>         <mi>n</mi>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\phi (n)}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb3dbe542ca7d51c4f32e32cefb8572edb26ab3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.589ex; height:2.843ex;" alt="{\\\\displaystyle \\\\phi (n)}"></span>, and may also be called <b>Euler's phi function</b>. In other words, it is the number of integers <span class="texhtml mvar" style="font-style:italic;">k</span> in the range <span class="texhtml">1 ≤ <i>k</i> ≤ <i>n</i></span> for which the greatest common divisor <span class="texhtml">gcd(<i>n</i>, <i>k</i>)</span> is equal to 1. The integers <span class="texhtml mvar" style="font-style:italic;">k</span> of this form are sometimes referred to as totatives of <span class="texhtml mvar" style="font-style:italic;">n</span>.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">https://en.wikipedia.org/wiki/Euler%27s_totient_function</a>)"""@en, """En mathématiques, l'indicatrice d'Euler est une fonction arithmétique de la théorie des nombres, qui à tout entier naturel n non nul associe le nombre d'entiers compris entre 1 et n (inclus) et premiers avec n.
<br/>Elle intervient en mathématiques pures, à la fois en théorie des groupes, en théorie algébrique des nombres et en théorie analytique des nombres.
<br/>En mathématiques appliquées, à travers l'arithmétique modulaire, elle joue un rôle important en théorie de l'information et plus particulièrement en cryptologie. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Indicatrice_d%27Euler">https://fr.wikipedia.org/wiki/Indicatrice_d%27Euler</a>)"""@fr ;
  skos:broader psr:-W90JFV07-V ;
  dc:modified "2024-10-18"^^xsd:date .