IMO 1989 LL VIE110
Do there exist two sequences of real numbers {ai}, {bi}, i \in
IMO 1989 LL VIE110
Origin: VIE
Problem
Do there exist two sequences of real numbers {ai}, {bi}, i \in N = {1, 2, 3, . . .}, satisfying the following conditions: 3\pi 2 \leqai \leqbi, cos aix + cos bix \geq−1 i for all i \inN and all x, 0 < x < 1?