ILL 1987 Problem 77

Find the least positive integer $k$ such that for any $a \in [0, 1]$ and any positive integer $n,$ $a^k(1 - a)^n < \frac{1}{(n+1)^3}.$

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Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.