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Let f(x) be a polynomial with rational coefficients and \alpha be a real number such that \alpha^3 - \alpha = [f(\alpha)]^3 - f(\alpha) = 33^{1992}. Prove that for each n \geq 1, \left [ f^{n}(\alpha) \right]^3 - f^{n}(\alpha) = 33^{1992}, where f^{n}(x) = f(f(\cdots f(x))), and n is a positive integer.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
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