On Arithmetic Progressions and a Proof of the Nonexistence of Magic Squares of Squares

2025/10/09 by Oscar Hill, Hill, Oscar
Computer Science · Engineering · Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Graph Labeling and Dimension Problems #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2510.08286

openalex publication_date 2025/10/09 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/31

Abstract

We explore some of the properties of consecutive, equally-summed arithmetic progressions of odd numbers, particularly their offsets and sums, before using them to prove that no 3×3 magic squares of distinct square integers exist.

Related

• On the 3 × 3 magic square constructed with nine distinct square numbers
• Arithmetic progressions of squares, cubes and n-th powers
• Squares in arithmetic progressions and infinitely many primes
• Existence of K-multimagic squares and magic squares of kth powers with distinct entries
• On the Construction of Doubly Even Order Magic Squares