On the number of solutions of the generalized Ramanujan-Nagell equation D₁x²+D₂^m=2ⁿ⁺²

2013/04/12 by Jianghua Li, Li Jianghua, Jianghua, Li
Mathematics · #11D61 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D61

paper · pdf · doi:10.48550/arxiv.1304.3530

16 pages, 0 figures

arxiv created 2013/04/12 · openalex publication_date 2013/04/12 · arxiv updated 2013/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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+D₂^m=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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