A New Transformation of the Magic Square of Squares

Abstract

We show arithmetic triplets of Gaussian squares are in 3-to-1 correspondence with Pythagorean triples thereof. This correspondence would transform a solution to the Magic Square of Squares puzzle into a larger structure of perfect Gaussian squares. In particular, we obtain the backwards result that a puzzle solution would generate non-trivial near-miss solutions in the Gaussian integers. Results are applied to popular near-misses.