Parametrization of Pythagorean triples by a single triple of polynomials
arXiv:0706.0290 · doi:10.1016/j.jpaa.2007.05.019
Abstract
It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials.
to appear in J. Pure Appl. Algebra
References in corpus (1)
Cited by in corpus (5)
- Remarks on polynomial parametrization of sets of integer points
- A new parameterisation of Pythagorean triples in terms of odd and even series
- Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples
- Ehrhart polynomial for lattice squares, cubes and hypercubes
- The Triangular Theorem of the Primes: Binary Quadratic Forms and Primitive Pythagorean Triples