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Maximum Minimum Cyclic Product Differences

2175ExpertAlgebraInequalities

PRÉPARATION OLYMPIQUE FRANÇAISE DE MATHÉMATIQUES - ENVOI 2 : AlgèBre

Let $n \geqslant 2$ and $a_{1}, \ldots, a_{n} \in [0,1]$ be real numbers. Determine the maximum possible value of the smallest of the numbers $$ a_{1}-a_{1} a_{2},\ a_{2}-a_{2} a_{3},\ \ldots,\ a_{n}-a_{n} a_{1} $$
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