International Competitions Tuymaada Yakut Olympiad 2009
International Competitions Tuymaada Yakut Olympiad 2009
International Competitions Tuymaada Yakut Olympiad 2009
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<strong>Tuymaada</strong> <strong>Yakut</strong> <strong>Olympiad</strong> <strong>2009</strong><br />
4 Determine the maximum number h satisfying the following condition: for every a ∈ [0, h] and<br />
every polynomial P (x) of degree 99 such that P (0) = P (1) = 0, there exist x 1 , x 2 ∈ [0, 1]<br />
such that P (x 1 ) = P (x 2 ) and x 2 − x 1 = a.<br />
Proposed by F. Petrov, D. Rostovsky, A. Khrabrov<br />
This file was downloaded from the AoPS Math <strong>Olympiad</strong> Resources Page Page 4<br />
http://www.artofproblemsolving.com/
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