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$f(n)$ divides $f(2^n) -2^{f(n)}$

Source: Indian TST 4 P1

July 17, 2019
number theorypolynomial

Problem Statement

Determine all non-constant monic polynomials f(x)f(x) with integer coefficients for which there exists a natural number MM such that for all n≥Mn \geq M, f(n)f(n) divides f(2n)−2f(n)f(2^n) - 2^{f(n)} Proposed by Anant Mudgal
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