A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations

We describe a computationally efficient approach to resolving equations of the form C 1 x 2 + C 2 = y n in coprime integers, for fixed values of C 1 , C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.