Result: Monochromatic 4-AP avoidance in 2 colorings of Z/𝑝Z for primes 5 ≤ 𝑝 ≤ 997

Title:
Monochromatic 4-AP avoidance in 2 colorings of Z/𝑝Z for primes 5 ≤ 𝑝 ≤ 997
Authors:
Irawan, Keane Maverick
Publisher Information:
Zenodo
Publication Year:
2025
Collection:
Zenodo
Subject Terms:
arithmetic progressions, combinatorial number theory, combinatorics, SAT, DRAT, dihedral actions, Ramsey theory
Document Type:
Report report
Language:
English
Relation:
https://zenodo.org/records/17137341; oai:zenodo.org:17137341; https://doi.org/10.5281/zenodo.17137341
DOI:
10.5281/zenodo.17137341
Availability:
https://doi.org/10.5281/zenodo.17137341
https://zenodo.org/records/17137341
Rights:
Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode ; Copyright (C) 2025 The Authors
Accession Number:
edsbas.907D6BDD
Database:
BASE

Further Information

We study 2-colorings of Z/pZ that avoid monochromatic 4-term arithmetic progressions for every step d with p not dividing d. We completely classify all primes 5<=p<=997: such a coloring exists exactly for p in {5,7,11}. When solutions exist, the minimal period equals p, and we enumerate all solutions up to dihedral symmetries and global color swap. For nonexistence (13<=p<=997) we provide DRAT-verified UNSAT certificates. The artifact includes Python scripts, CNF encodings, solver logs, DRAT proofs, and word lists for exact reproduction. Code and data: https://github.com/weebyesyes/Primes-paper-repo