On Monochromatic Solutions of Linear Equations Using At Least Three Colors

Laurence P. Wijaya

On Monochromatic Solutions of Linear Equations Using At Least Three Colors

Combinatorics 2025-06-27 v3 Number Theory

Authors: Laurence P. Wijaya

Abstract

We study the number of monochromatic solution to linear equation in $\{1,\dots,n\}$ when we color the set by at least three colors. We consider the $r$ -commonness for $r\geq 3$ of linear equation with odd number of terms, and we also prove that any $2$ -uncommon equation is $r$ -uncommon for any $r\geq 3$ .

Keywords

monochromatic solutions linear equations colorings Rado's theorem uncommon equations combinatorial number theory

Cite

@article{arxiv.2501.17136,
  title  = {On Monochromatic Solutions of Linear Equations Using At Least Three Colors},
  author = {Laurence P. Wijaya},
  journal= {arXiv preprint arXiv:2501.17136},
  year   = {2025}
}

Comments

Accepted to INTEGERS

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