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2010 USAMO Problems/Problem 3

Revision as of 22:17, 4 May 2010 by Aopsvd (talk | contribs) (Created page with '==Problem== The <math>2010</math> positive numbers <math>a_1, a_2, \ldots , a_{2010}</math> satisfy the inequality <math>a_ia_j \le i+j</math> for all distinct indices <math>i, j…')
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Problem

The $2010$ positive numbers $a_1, a_2, \ldots , a_{2010}$ satisfy the inequality $a_ia_j \le i+j$ for all distinct indices $i, j$. Determine, with proof, the largest possible value of the product $a_1a_2\cdots a_{2010}$.

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