Magic sets for polynomials of degree n

Let P-n be the family of all real, non-constant polynomials with degree at most n and let Q(n) be the family of all complex, non-constant polynomials with degree at most n. A set S subset of R is called a set of range uniqueness (SRU) for a family F is an element of {P-n, Q(n)} if for all f, g is an element of F, f[S] = g[S] double right arrow f = g. And S is called a magic set if for all f, g is an element of F, f[S] subset of g[S] double right arrow f = g. In this paper we will show that there are magic sets for P-n and Q(n) of size s for every s >= 2n + 1. However, there are no SRUs of size at most 2n for P-n and Q(n). Moreover we will show that SRUs and magic sets are not the same by giving examples of SRUs for P-2 and P-3 that are not magic. (C) 2020 Elsevier Inc. All rights reserved.