olymmath

Putnam 2023 A1

  • Session A

For a positive integer nn, let fn(x)=cos⁡(x)cos⁡(2x)cos⁡(3x)⋯cos⁡(nx)f_n(x) = \cos(x) \cos(2x) \cos(3x) \cdots \cos(nx). Find the smallest nn such that ∣fn′′(0)∣>2023|f_n''(0)| > 2023.

Curated text Kedlaya Putnam archive. Quoted with source.

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