TY - JOUR
T1 - Polynomial parametrization of pythagorean tuples
AU - Vaserstein, Leonid
AU - Sakkalis, Takis
AU - Frisch, Sophie
PY - 2010/9/1
Y1 - 2010/9/1
N2 - A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (xi) ∈ Ak+l, where k, l ∈ , k < l which satisfies σi = 1k xi2 = σi= 1lk+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.
AB - A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (xi) ∈ Ak+l, where k, l ∈ , k < l which satisfies σi = 1k xi2 = σi= 1lk+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.
UR - http://www.scopus.com/inward/record.url?scp=77957550836&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77957550836&partnerID=8YFLogxK
U2 - 10.1142/S1793042110003496
DO - 10.1142/S1793042110003496
M3 - Article
AN - SCOPUS:77957550836
SN - 1793-0421
VL - 6
SP - 1261
EP - 1272
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 6
ER -