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polynomial |f(k)-t^k)<1, bound degree

Source: IMOC 2019 A2

August 18, 2021
algebrapolynomial

Problem Statement

Given a real number t≥3t\ge3, suppose a polynomial f∈R[x]f\in\mathbb R[x] satisfies ∣f(k)−tk∣<1,∀k=0,1,…,n.\left|f(k)-t^k\right|<1,\enspace\forall k=0,1,\ldots,n.Prove that deg⁡f≥n\deg f\ge n.
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