The work of Cohn [Coh93] and Bugeaud, Mignotte and Siksek [BMS06] solves the Lebesgue-Naguel equation x2 + D = yn, x, y integers, n ≥ 3 for D a integer in the range 1 ≤ D ≤ 100. We propose to do the same for D in the range -100 ≤ D ≤ -1. For that we will use techniques that go from the most classical ones, ideal factorization over number fields and Thue equations, to the most modern approach to Diophantine equations, Frey curves and the Modular approach, passing by linear forms in logarithms.