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Non integer polynomial f

Source: Problem 5, Brazilian MO 2015

October 20, 2015
algebra proposedalgebrapolynomial

Problem Statement

Is that true that there exist a polynomial f(x)f(x) with rational coefficients, not all integers, with degree n>0n>0, a polynomial g(x)g(x), with integer coefficients, and a set SS with n+1n+1 integers such that f(t)=g(t)f(t)=g(t) for all tāˆˆSt \in S?
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