MAGIC SQUARES OF SQUARES
Paul Pierrat, Paul A. Zimmermann · 2015
All rows and columns and the two main diagonals sum up to 8515. Contrary to classical magic squares filled with consecutive integers, the only rule is that all elements are squares of different positive integers. We also require the magic square to be primitive, i.e., the gcd of all elements is one (indeed, multiplying all elements by some integer k keeps the equality between sums). In 1996, Martin Gardner asked whether there exists a 3 × 3 magic square filled with squares, and offered a $100 prize to the first discoverer. Euler’s method, and a detailed history of this problem is presented in [2]. Lee Sallows found in 1997 the following near miss: