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finite set M of nonzero real numbers

Source: All-Russian Olympiad 1996, Grade 11, Second Day, Problem 7

April 19, 2013
algebrapolynomialinequalitiesalgebra proposed

Problem Statement

Does there exist a finite set MM of nonzero real numbers, such that for any natural number nn a polynomial of degree no less than nn with coeficients in MM, all of whose roots are real and belong to MM?
E. Malinnikova
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