MathDB
a^2_1 + a^2_2 + ... + a^2_100 = 1

Source: IMO Shortlist 2007, A6, AIMO 2008, TST 7, P1

July 13, 2008
inequalitiesIMO Shortlist

Problem Statement

Let a1,a2,…,a100 a_1, a_2, \ldots, a_{100} be nonnegative real numbers such that a^2_1 \plus{} a^2_2 \plus{} \ldots \plus{} a^2_{100} \equal{} 1. Prove that a^2_1 \cdot a_2 \plus{} a^2_2 \cdot a_3 \plus{} \ldots \plus{} a^2_{100} \cdot a_1 < \frac {12}{25}. Author: Marcin Kuzma, Poland
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