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greater than 1995

Source: Vietnam NMO 1995, Problem 5

September 7, 2008
algebrapolynomialalgebra proposed

Problem Statement

Find all poltnomials P(x) P(x) with real coefficients satisfying: For all a>1995 a>1995, the number of real roots of P(x)\equal{}a (incuding multiplicity of each root) is greater than 1995, and every roots are greater than 1995.
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