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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Can a non-surjective polynomial map from an infinite field to itself miss only finitely many...
(My field theory is very weak, so I'm not sure how obviously correct or obviously incorrect these assumptions are):
There is a sequence of finite fields $F_q$ with appropriate polynomials $f_q$ such that …