olymmath

IMO 1988 Problem 4

  • Day 2

Show that the solution set of the inequality ∑k=170kx−k≥54\sum^{70}_{k = 1} \frac {k}{x - k} \geq \frac {5}{4} is a union of disjoint intervals, the sum of whose length is 1988.

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1988 official English paper, page 2.

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