A magic square is a square grid of numbers where each row, column, and long diagonal has the same sum (called the magic sum). An open problem popularized by Martin Gardner asks whether there exists a 3×3 magic square of distinct positive square numbers. In this paper, we expand on existing results about the prime factors of elements of such a square, and then provide a full list of the ways a prime factor could appear in one. We also suggest a separate possible computational approach based on the prime signature of the center entry of the square.
"Some Thoughts on The 3 × 3 Magic Square of Squares Problem,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 24:
1, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss1/7