Problem 18

Algebra Level 4

A=(1+a2)2(1+a3)3(1+a2016)2016B=20162016 \begin{aligned} A &= &(1+a_2)^2 (1+a_3)^3 \cdots (1+a_{2016})^{2016} \\ B &=& 2016^{2016} \end{aligned}

Given that a2,a3,,a2016a_2, a_3, \ldots, a_{2016} are non-negative real numbers such that their product is 1, and let AA and BB as described above.

Which of the following equation/inequation must be true?

This problem inspired of IMO problem in a few year back.
This problem is in this Set.

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