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2

Part of 2017 International Olympic Revenge

Problems(1)

IMOR 2017 - Problem 2

Source: 1st International Mathematical Olympic Revenge

7/22/2017
A polynomial is good if it has integer coefficients, it is monic, all its roots are distinct, and there exists a disk with radius 0.990.99 on the complex plane that contains all the roots. Prove that there is no good polynomial for a sufficient large degree.
Proposed by Rodrigo Sanches Angelo (rsa365), Brazil.
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