The solution of 𝑦²+²ⁿ=𝑥³

Abstract

All solutions to the diophantine equation ( ∗ ) y 2 + γ 2 n = x 3 ; γ = ± 1 , \begin{equation}\tag {$\ast $}{y^2} + \gamma {2^n} = {x^3};\quad \gamma = \pm 1,\end{equation} are found.