A published paper or arXiv preprint answers the main question of Erdős Problem #521 (theorem erdos_521 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Let (\epsilon_k)_{k\geq 0} be independently uniformly chosen at random from \{-1,1\}. If R_n counts the number of real roots of f_n(z)=\sum_{0\leq k\leq n}\epsilon_k z^k then is it true that, almost surely, \lim_{n\to \infty}\frac{R_n}{\log n}=\frac{2}{\pi}? The answer is no: this almost-sure limit fails. This result was obtained first by others, who deserve the credit for the problem; the link is to an independent machine-checked proof by Star Fleet Math.