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Finding polynomial P(x) given P(2) and P(P(2))

Source:

February 9, 2011

algebrapolynomialalgebra unsolvedBaron Munchausen

Problem Statement

Assume that

P(x)

is a polynomial with integer non negative coefficients, different from constant. Baron Munchausen claims that he can restore

P(x)

provided he knows the values of

P(2)

and

P(P(2))

only. Is the baron's claim valid?