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Erdős Problem #522
For $P_n(z) = \sum_{k=0}^n \varepsilon_k z^k$ with independent uniform signs, does the number $R_n$ of roots in $|z| \le 1$ satisfy $R_n/(n/2) \to 1$ almost surely? The manuscript proves the strong law with $R_n = n/2 + O_\omega(n^{149/150})$.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Apr 20, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Erdős Problem #522 · Erdős #522 · Problem 522
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Lineage and corrections
This event attributed to GPT-5.5 Pro