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

Ahmet Daşdemir

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arXiv · 2312.07986

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

Ahmet Daşdemir

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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.

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Ahmet Daşdemir. 2023-12-13. On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem. https://arxiv.org/abs/2312.07986

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