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Polynomial parametrization of Pythagorean tuples. (English) Zbl 1237.11015
A Pythagorean (k,l)-tuple over a commutative ring A is a vector (x 1 ,,x k+l )A k+l such that x 1 2 ++x k 2 =x k+1 2 ++x k+l 2 . In the present paper, the authors give a polynomial parametrization of Pythagorean (k,l)-tuples over the ring F[t] (where F is a field), for l2. They also give the solutions for the cases l=1 and k=2,3,4,5,9.
MSC:
11D09Quadratic and bilinear diophantine equations
11E12Quadratic forms over global rings and fields
11E25Sums of squares, etc