Putnam 1972 B6

B-6. Let $n_{1}<n_{2}<n_{3}<\cdots<n_{k}$ be a set of positive integers. Prove that the polynomial $1+z^{n_{1}}$ $+z^{n_{2}}+\cdots+z^{n_{k}}$ has no roots inside the circle $|z|<(\sqrt{5}-1) / 2$.