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OP-4549SolvedMathematics · general

Erdős Problem 524: Analysis exact value and asymptotic bounds

TheoremDB P10420 · background embedded json fragment

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓
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Problem statement

For any t∈(0,1)t\in (0,1) let t=∑k=1∞ϵk(t)2−kt=\sum_{k=1}^\infty \epsilon_k(t)2^{-k} (where ϵk(t)∈{0,1}\epsilon_k(t)\in \{0,1\}). What is the correct order of magnitude (for almost all t∈(0,1)t\in(0,1)) for Mn(t)=max⁡x∈[−1,1]∣∑k≤n(−1)ϵk(t)xk∣?M_n(t)=\max_{x\in [-1,1]}\left\lvert \sum_{k\leq n}(-1)^{\epsilon_k(t)}x^k\right\rvert?.

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Resolved. Not Lean-verified

References
  1. [1]TheoremDB P10420 link

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