1 Ocak 2017 Dergi makalesi Açık Erişim

Keskin, Refik; Duman, Merve Guney

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{
  "@context": "https://schema.org/", 
  "@id": 47301, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Sakarya Univ, Math Dept, TR-54187 Sakarya, Turkey", 
      "name": "Keskin, Refik"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Sakarya Univ, Math Dept, TR-54187 Sakarya, Turkey", 
      "name": "Duman, Merve Guney"
    }
  ], 
  "datePublished": "2017-01-01", 
  "description": "Let k >= 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.", 
  "headline": "A NOTE ON SOME DIOPHANTINE EQUATIONS", 
  "identifier": 47301, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "A NOTE ON SOME DIOPHANTINE EQUATIONS", 
  "url": "https://aperta.ulakbim.gov.tr/record/47301"
}