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Polynomial with power of two

Source: 2017 Taiwan TST Round 1

April 13, 2018
algebrapolynomial

Problem Statement

Let nn be an odd number larger than 1, and f(x)f(x) is a polynomial with degree nn such that f(k)=2kf(k)=2^k for k=0,1,⋯ ,nk=0,1,\cdots,n. Prove that there is only finite integer xx such that f(x)f(x) is the power of two.
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