On the number of solutions of the generalized Ramanujan-Nagell equation

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Applications of the Hypergeometric Method to the Generalized Ramanujan-Nagell Equation (2002, methodology): “The case y = 2 has been admirably treated by Beukers [10] and Le [21, 23], culminating in the following”
Divisibility of the class numbers of imaginary quadratic fields (2017, background): “Shorey [2] on Diophantine equations which is one of the main ingredient in the proof of Theorem 1.”
Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation (2004, background): “…has exactly five solutions with x 1 (see [Mig84] for a very simple proof) and is, in this respect, singular: indeed, Bugeaud and Shorey [BS01] established that (4) with D positive and k a prime number not dividing D has at most two solutions in positive integers x, n, except for (D, k) = (7, 2).”
Ternary Diophantine Equations via Galois Representations and Modular Forms (2004, background): “One such approach involves replacing 7 by any fixed odd integer; in this situation, the definitive result is the following, combining theorems of Beukers [2] and Le [34], [35].”