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Let n\ge 3 be an integer, and let a_2,a_3,\ldots ,a_n be positive real numbers such that a_{2}a_{3}\cdots a_{n}=1. Prove that
(1 + a_2)^2 (1 + a_3)^3 \dotsm (1 + a_n)^n > n^n.

Proposed by Angelo Di Pasquale, Australia

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