A Note on the Diophantine Equation $D_1x^2+D_2=ak^n$

[摘要] We consider the generalized Ramanujan-Nagell Diophantine equation, which was solved by Bugeaud and Shorey in 2001. However, a counterexample was found by Leu and Li in 2003. We provide another counterexample and show that both the example herein and the latter are results of Ljunggren from the 1940s. Given that these are all the omissions in the Bugeaud-Shorey work, this secures the study of the generalized Ramanujan-Nagell equation.

[学科分类] 数学（综合）

[关键词] Ramanujan-Nagell equations.