1 Ocak 2017 Dergi makalesi Açık Erişim

Keskin, Refik; Duman, Merve Guney

Citation Style Language JSON

{
  "DOI": "10.18514/MMN.2017.1857", 
  "abstract": "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.", 
  "author": [
    {
      "family": "Keskin", 
      "given": " Refik"
    }, 
    {
      "family": "Duman", 
      "given": " Merve Guney"
    }
  ], 
  "container_title": "MISKOLC MATHEMATICAL NOTES", 
  "id": "47301", 
  "issue": "1", 
  "issued": {
    "date-parts": [
      [
        2017, 
        1, 
        1
      ]
    ]
  }, 
  "page": "235-249", 
  "title": "A NOTE ON SOME DIOPHANTINE EQUATIONS", 
  "type": "article-journal", 
  "volume": "18"
}