Order three magic squares of distinct squared integers are studied. We show that such a magic square is not possible if the smallest entry is the square of a prime number, or unity. A method for generating all arithmetic progressions of three squared integers whose smallest term is the square of a prime or unity is presented via a set of linear transformation matrices involving the Pell numbers.

magic square, Pell numbers.

Received: September 2, 2024; Revised: September 20, 2024; Accepted: October 10, 2024; Published: October 22, 2024

How to cite this article: D. N. Coumbe, Magic squares of perfect squares and Pell numbers, JP Journal of Algebra, Number Theory and Applications 63(6) (2024), 587-614. https://doi.org/10.17654/0972555524032

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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