An elementary approach to the generalized Ramanujan–Nagell equation

Elif Kızıldere Mutlu (), Maohua Le () and Gökhan Soydan ()
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Elif Kızıldere Mutlu: Bursa Uludağ University
Maohua Le: Lingnan Normal College
Gökhan Soydan: Bursa Uludağ University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 392-399

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

Keywords: Polynomial-exponential Diophantine equation; Generalized Ramanujan–Nagell equation; Elementary method in number theory; 11D61; 11D41 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00372-8

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