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.

Author Bio

Desmond Weisenberg graduated from Case Western Reserve University in 2022, majoring in mathematics and minoring in computer science and bioethics/medical humanities. He worked on this paper independently with the support of Dr. Long Tran in the spring of 2022.

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