Exploring 2012 Imo Problem 2 Two Solutions

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https://artofproblemsolving.com/community/c3839_2012_imo. IMO 2012 Can you prove that (a₂ + 1)²(a₃ + 1)³⋯(aₙ + 1)ⁿ ≥ nⁿ given that a₂a₃⋯aₙ = 1 ? At first glance, this inequality looks ... evaluating the product.

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