PreprintCC BY-NC-ND 4.0arXiv
The Fibonacci numbers are not 3-accessible
Abstract
A D-diffsequence is a sequence of integers x1 < … < xk such that xi+1 −xi ∈ D for 1 ≤ i ≤ k−1. The set D is called r-accessible if every r-coloring of the positive integers contains arbitrarily long monochromatic D-diffsequences. This note proves that the set of Fibonacci numbers is not 3-accessible, resolving an open problem of Landman and Robertson from 2007.
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BibTeX
@misc{wesley2026fibonacci,
title = {{The Fibonacci numbers are not 3-accessible}},
author = {William J. Wesley},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33744},
eprint = {2609.33744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33744},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Fibonacci numbers are not 3-accessible
AU - William J. Wesley
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33744
UR - https://arxiv.org/abs/2609.33744
AB - A D-diffsequence is a sequence of integers x_1 < … < x_k such that x_i+1 −x_i ∈ D for 1 ≤ i ≤ k−1. The set D is called r-accessible if every r-coloring of the positive integers contains arbitrarily long monochromatic D-diffsequences. This note proves that the set of Fibonacci numbers is not 3-accessible, resolving an open problem of Landman and Robertson from 2007.
ER -