Monochromatic 4-AP avoidance in 2-colorings of Z/pZ for primes 5 <= p <= 997
Keane Maverick Irawan
公開日: 2025/9/17
Abstract
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 if and only if p is in {5, 7, 11}. For larger primes, nonexistence is consistent with lower bounds of Wolf and Lu--Peng on the number of monochromatic 4-APs in 2-colorings of Z_p. When solutions exist, the minimal period equals p, and we enumerate them up to dihedral symmetries and a global color swap. The proofs combine residue-class checks with small structural observations and SAT certificates for nonexistence (DRAT-verified). All scripts and proof logs are provided for exact reproduction.