JP Journal of Algebra, Number Theory and Applications
Volume 8, Issue 1, Pages 69 - 80
(June 2007)
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MATRIX GENERATION OF THE DIOPHANTINE SOLUTIONS TO SUMS OF SQUARES THAT ARE SQUARE
Jordan O. Tirrell (U. S. A.) and Clifford A. Reiter (U. S. A.)
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Abstract: 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. |
Keywords and phrases: sums of squares, Barning Tree. |
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