An elementary approach to the generalized Ramanujan–Nagell equation

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Mutlu E. K., Le M., Soydan G.

Indian Journal of Pure and Applied Mathematics, cilt.55, sa.1, ss.392-399, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s13226-023-00372-8
  • Dergi Adı: Indian Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Sayfa Sayıları: ss.392-399
  • Anahtar Kelimeler: Polynomial-exponential Diophantine equation, Generalized Ramanujan-Nagell equation, Elementary method in number theory
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

.Let k be a fixed positive integer with k> 1. In this paper, using various elementary methods in number theory, we give criteria under which the equation x2+ (2 k- 1 ) y= kz has no positive integer solutions (x, y, z) with y∈ { 3 , 5 }.