IMO 1984 LL MON35

Prove that there exist distinct natural numbers m1, m2, . . . ,

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IMO 1984 LL MON35

Origin: MON

Problem

Prove that there exist distinct natural numbers m1, m2, . . . , mk satisfying the conditions \pi−1984 < 25 −  1 m1

  • 1 m2
  • \cdot \cdot \cdot + 1 mk  < \pi−1960 where \pi is the ratio between circle and its diameter.