Matrix generation of the diophantine solutions to sums of 3 [less than or equal to] n [less than or equal to] 9 squares that are square
Tirrell, J. O.; Reiter, Clifford A.
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 3 [less than or equal to] n [less than or equal to] 8 all the
Diophantine solutions may be obtained via matrix multiplication from a
single type of initial solution. For n = 9 two different types of initial
solutions are required.
↧