olymmath

Putnam 2018 B2

  • Session B

Let nn be a positive integer, and let fn(z)=n+(n−1)z+(n−2)z2+⋯+zn−1f_n(z) = n + (n-1) z + (n-2)z^2 + \cdots + z^{n-1}. Prove that fnf_n has no roots in the closed unit disk {z∈C ⁣:∣z∣≤1}\{z \in \mathbb{C}\colon |z| \leq 1 \}.

Curated text Kedlaya Putnam archive. Quoted with source.

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