Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the Diophantine Equations $J_n +J_m =L_k$ and $L_n +L_m =J_k$ (2409.09791v4)

Published 15 Sep 2024 in math.NT

Abstract: This paper finds all Lucas numbers which are the sum of two Jacobsthal numbers. It also finds all Jacobsthal numbers which are the sum of two Lucas numbers. In general, we find all non-negative integer solutions $(n, m, k)$ of the two Diophantine equations $L_n +L_m =J_k$ and $J_n +J_m =L_K,$ where $\left\lbrace L_{k}\right\rbrace_{k\geq0}$ and $\left\lbrace J_{n}\right\rbrace_{n\geq0}$ are the sequences of Lucas and Jacobsthal numbers, respectively. Our primary results are supported by an adaption of the Baker's theorem for linear forms in logarithms and Dujella and Peth\H{o}'s reduction method.

Summary

We haven't generated a summary for this paper yet.