Chen, Xigeng; Guo, Yongdong; Le, Maohua On the number of solutions of the generalized Ramanujan-Nagell equation \(x^2+D=k^n\). (Chinese. English summary) Zbl 1005.11010 Acta Math. Sin. 41, No. 6, 1249-1254 (1998). Summary: Let \(D\), \(k\) be positive integers with \(\gcd (D,k)= 1\). In this paper, using elementary methods, we prove that if \(D\) is a prime, then the equation \(x^2+ D= k^n\) has at most eight positive integer solutions \((x,n)\). MSC: 11D61 Exponential Diophantine equations 11D45 Counting solutions of Diophantine equations Keywords:generalized Ramanujan-Nagell equation; exponential Diophantine equation; number of solutions; upper bound PDFBibTeX XMLCite \textit{X. Chen} et al., Acta Math. Sin. 41, No. 6, 1249--1254 (1998; Zbl 1005.11010)