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Problem 2 IMC 2004 Macedonia

Source:

July 25, 2004
algebrapolynomialinductionIMCcollege contests

Problem Statement

Let f1(x)=x2−1f_1(x)=x^2-1, and for each positive integer n≥2n \geq 2 define fn(x)=fn−1(f1(x))f_n(x) = f_{n-1}(f_1(x)). How many distinct real roots does the polynomial f2004f_{2004} have?
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