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Three numbers among 1400 given numbers have certain property

Source: 2021 Iran second round mathematical Olympiad P5

May 16, 2021
combinatoricsalgebrainequalitiesIran

Problem Statement

1400 real numbers are given. Prove that one can choose three of them like x,y,zx,y,z such that : ∣(x−y)(y−z)(z−x)x4+y4+z4+1∣<0.009\left|\frac{(x-y)(y-z)(z-x)}{x^4+y^4+z^4+1}\right| < 0.009
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