On the Diophantine equation x2 + 2 = yn

By B. Sury. 2000

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Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers (2004, methodology): “The idea behind the proof is inspired by a method of Kraus (see [23] or [48]) but there are added complications in our situation: for any prime p the equation Fn = y has the solution (n, y) = (1, 1), and also the solution (n, y) = (−1, 1) (obtained by extrapolating the definition of the Fibonacci se”
The Modular Approach to Diophantine Equations (2007, methodology): “1, the method of Kraus and classical techniques for Diophantine equations recently lead to the complete solutions of equations x(2) + D = y for n ≥ 3 and 1 ≤ D ≤ 100 (see [9], [31]).”
Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation (2004, methodology): “The second method is adapted from the ideas of Kraus [26] (see also [51]).”