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there is a polynomial p(x) such that p(2 cos x) = 2 cos nx., for every n>0

Source: Vietnam MO 1979 P4

July 28, 2018
polynomialtrigonometryalgebra

Problem Statement

For each integer n>0n > 0 show that there is a polynomial p(x)p(x) such that p(2cosx)=2cosnxp(2 cos x) = 2 cos nx.
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