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Are all algebraic integers with absolute value 1 roots of unity?

Let $\alpha$ be an algebraic integer. Suppose that all the roots of its minimal polynomial have absolute value 1. Is $\alpha$ a root of unity?


marked as duplicate by Arturo Magidin, William, Andrés E. Caicedo, Sasha, user5783 Jul 28 '12 at 6:10

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