English

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

Number Theory 2019-12-23 v2

Abstract

We describe a computationally efficient approach to resolving equations of the form C1x2+C2=ynC_1x^2 + C_2 = y^n in coprime integers, for fixed values of C1C_1, C2C_2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.

Cite

@article{arxiv.1910.07453,
  title  = {A Lucas-Lehmer approach to generalised Lebesgue-Ramanujan-Nagell equations},
  author = {Vandita Patel},
  journal= {arXiv preprint arXiv:1910.07453},
  year   = {2019}
}

Comments

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