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, vol.55, no.1, pp.392-399, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s13226-023-00372-8
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Page Numbers: pp.392-399
  • Keywords: Polynomial-exponential Diophantine equation, Generalized Ramanujan-Nagell equation, Elementary method in number theory
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2023, The Indian National Science Academy.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 }.