Article

On the number of solutions of the generalized Ramanujan-Nagell equation D₁X² + D^M₂ = 2^N+2

Published in: Quaestiones Mathematicae
Volume 41 , issue 2 , 2018 , pages: 149–163

DOI: 10.2989/16073606.2016.1259186

Author(s): Jianghua Li College of Science, P.R.China

Keywords: 11D61 , 11D61

Abstract

Let D₁, D₂ be coprime odd integers with min (D₁, D₂) > 1, and let N (D₁, D₂) denote the number of positive integer solutions (x, m, n) of the equation D₁x²+D^m₂ = 2ⁿ⁺². In this paper, we prove that N (D₁, D₂) ≤ 2 except for N (3, 5) = N (5, 3) = 4 and N (13, 3) = N (31, 97) = 3.

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