1 Ocak 2017 Dergi makalesi Açık Erişim

Keskin, Refik; Duman, Merve Guney

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/47301</identifier>
  <creators>
    <creator>
      <creatorName>Keskin, Refik</creatorName>
      <givenName>Refik</givenName>
      <familyName>Keskin</familyName>
      <affiliation>Sakarya Univ, Math Dept, TR-54187 Sakarya, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Duman, Merve Guney</creatorName>
      <givenName>Merve Guney</givenName>
      <familyName>Duman</familyName>
      <affiliation>Sakarya Univ, Math Dept, TR-54187 Sakarya, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>A Note On Some Diophantine Equations</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2017</publicationYear>
  <dates>
    <date dateType="Issued">2017-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/47301</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.18514/MMN.2017.1857</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">Let k &amp;gt;= 3 be an odd integer. In this paper we investigate all positive integer solutions of the equations x(4) - kx(2) y + y(2) = -/+ A, x(4) kx(2) y + y(2) = -/+ A(k(2) - 4), x(4) - (k(2) - 4)y(2) = -/+ 4A, and x(2) - (k(2) - 4)y(4) = -/+ 4A with A = -/+(k -/+ 2). We show that if k = 1(mod8) and k(2) - 4 be a square-free integer; then the equation x(4) - kx(2) y + y(2) = (k - 2)(k(2) - 4) has no positive integer solutions. Moreover, if k(2) - 4 be a square-free integer; then the equation x(4) - kx(2) y + y(2) = -(k + 2)(k(2) - 4) has no positive integer solutions.</description>
  </descriptions>
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