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There exists interval whose elements satisfy inequality.

Source:

January 11, 2011

inequalities unsolvedinequalities

Problem Statement

Let

0 \le x_1 \le x_2\le\cdots\le x_n \le 1

. Prove that for all

A \ge 1

, there exists an interval

I

of length

2\sqrt[n]{A}

such that for all

x \in I

|(x - x_1)(x - x_2) \cdots (x -x_n)| \le A.