IMO Shortlist 1992 problem 19


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2. travnja 2012.
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Let f(x) = x^8 + 4x^6 + 2x^4 + 28x^2 + 1. Let p > 3 be a prime and suppose there exists an integer z such that p divides f(z). Prove that there exist integers z_1, z_2, \ldots, z_8 such that if g(x) = (x - z_1)(x - z_2) \cdot \ldots \cdot (x - z_8), then all coefficients of f(x) - g(x) are divisible by p.
Izvor: Međunarodna matematička olimpijada, shortlist 1992