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Z[x] on set of integers, bounding closure measure of set

Source: VJIMC 2013 1.3

May 31, 2021
Setsnumber theoryPolynomials

Problem Statement

Let SS be a finite set of integers. Prove that there exists a number cc depending on SS such that for each non-constant polynomial ff with integer coefficients the number of integers kk satisfying f(k)∈Sf(k)\in S does not exceed max⁡(deg⁡f,c)\max(\deg f,c).
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