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Existence of f(x) such that f(g(x))=g(f(x)).

Source: ILL 1979-42

June 2, 2011

quadraticsalgebrapolynomialalgebra unsolved

Problem Statement

Let a quadratic polynomial

g(x) = ax^2 + bx + c

be given and an integer

n \ge 1

. Prove that there exists at most one polynomial

f(x)

of

n

th degree such that

f(g(x)) = g(f(x)).

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