Geodesic
Variations on a Theme of Kronecker
Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 129-133

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In 1857, Kronecker [10] showed that if θ1,..., θn are the roots of the polynomial P(z)= zn |cn-1+ ... + cn, where c1, ..., cn are integers with cn≠0, and if |θ1| ≤ 1, ..., |θ1| ≤1, then θ1, ..., θn are roots of unity. The proof is short and ingenious: Consider the polynomials Pm(z) whose roots are The condition on the size of the roots and the fact that the ci are integers implies that there can only be a finite number of different Pm . Thus two distinct powers of each root must coincide and this means that each root is a root of unity. 
Boyd, David W. Variations on a Theme of Kronecker. Canadian mathematical bulletin, Tome 21 (1978) no. 2, pp. 129-133. doi: 10.4153/CMB-1978-023-x
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     title = {Variations on a {Theme} of {Kronecker}},
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     year = {1978},
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     doi = {10.4153/CMB-1978-023-x},
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