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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory