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How many nonzero coefficients can a polynomial

Source: IMC 2007, Day 1, Problem 6

August 6, 2007
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Problem Statement

How many nonzero coefficients can a polynomial P(x) P(x) have if its coefficients are integers and ∣P(z)∣≤2 |P(z)| \le 2 for any complex number z z of unit length?
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