Jordan O. Tirrell and Clifford A. Reiter, Matrix Generation of the Diophantine solutions to sums of 3 ≤ n ≤ 9 squares that are square, JP Journal of Algebra, Number Theory and Applications, 8 1 (2007) 69-80.

Pythagorean Triples are well-known examples of integer solutions to sums of two squares giving another square. It is well known that Pythagorean Triples may be generated parametrically. It is somewhat less well known that they may also be generated via matrices. In this note we describe how matrix generators may be used to produce all the Diophantine solutions of a square being a sum of squares when the number of squares in the sum is between 3 and 9. For all the Diophantine solutions may be obtained via matrix multiplication from a single type of initial solution. For two different types of initial solutions are required.

See Also: · Preprint of the manuscript. · Abstract for related manuscript "Pursuing the Perfect Parallelepiped". · [Abstract][Preprint] for related manuscript "Generalized Perfect Parallelograms and Their Matrix Generators". · [Materials] for related manuscript "Perfect Parallelepipeds Exist".