MathDB

B6

Part of 1972 Putnam

Problems(1)

Putnam 1972 B6

Source:

6/5/2008
Let n1<n2<n3<⋯<nk n_1<n_2<n_3<\cdots <n_k be a set of positive integers. Prove that the polynomial 1\plus{}z^{n_1}\plus{}z^{n_2}\plus{}\cdots \plus{}z^{n_k} has no roots inside the circle |z|<\frac{\sqrt{5}\minus{}1}{2}.
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