On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem

Ahmet Daşdemir

On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem

Number Theory 2024-01-31 v3

Authors: Ahmet Daşdemir

Abstract

In this paper, we deal with Diophantine equations $N = {F_k}^3 + {F_\ell }^3 = {F_m}^3 + {F_n}^3$ and $M = {L_k}^3 + {L_\ell }^3 = {L_m}^3 + {L_n}^3$ . In other words, we discover the Fibonacci and Lucas numbers that are also Hardy-Ramanujan numbers.

Keywords

Diophantine equations Fibonacci numbers Lucas numbers Hardy-Ramanujan problem sums of cubes

Cite

@article{arxiv.2312.07986,
  title  = {On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem},
  author = {Ahmet Daşdemir},
  journal= {arXiv preprint arXiv:2312.07986},
  year   = {2024}
}

Comments

It contains some errors and so it will be developed more

Related papers

View all related →