Problem Set 2

Created on September 17, 2026

2026   ·   analysis   putnam   ·   weekly-problem-set

For the meeting Thursday, September 24.

Email solutions here.

Problem 1: Putnam 2018, B2

Let \(n\) be a positive integer, and let \(f_n(z) = n+(n-1)z+(n-2)z^2+\cdots+z^{n-1}\). Prove that \(f_n\) has no roots in the closed unit disk \(\lbrace z \in \mathbb{C} : \lvert z \rvert \leq 1 \rbrace\).

Problem 2: Putnam 2010, B5

Is there a strictly increasing function \(f : \mathbb{R} \to \mathbb{R}\) such that \(f'(x) = f(f(x))\) for all \(x\)?