olymmath

Putnam 1985 A5

  • Session A

Let Im=∫02πcos⁡(x)cos⁡(2x)⋯cos⁡(mx)dxI_m = \int_0^{2\pi} \cos(x)\cos(2x)\cdots \cos(mx) dx. For which integers mm, 1≤m≤101 \leq m \leq 10 is Im≠0I_m \neq 0?

Curated text Kedlaya Putnam archive. Quoted with source.

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