We find all rational solutions to the equation , where or . These are the two unsolved cases for in the range . Our method is elementary and can be applied to other situations to find all rational points on certain curves of genus .
"On the equation $y^2=x^6+k$." Rocky Mountain J. Math. 50 (6) 2167 - 2178, December 2020. https://doi.org/10.1216/rmj.2020.50.2167