On a Sufficient and Necessary Condition for a Multivariate Polynomial to Have Algebraically Dependent Roots - an Elementary Proof
نویسندگان
چکیده
In the paper we prove that a multivariate polynomial has algebraically dependent roots iff the coefficients are algebraic numbers up to a common proportional term. A complex analytic proof can be found in [2] with applications in the theory of linear functional equations, see also [3, an open problem, section 4.4] and [1]. Here we present an elementary proof involving cardinality properties and basic linear algebra.
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