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

Abstract

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.

9 pages. Theorem now deals with small primes $p=7,11,13$. Duplicates in table of solutions have also been removed