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Find the least positive integer value of nnn such that for any nnn positive reals a1,a2,…,ana_{1},a_{2},\ldots,a_{n}a1,a2,…,an, we have
a12+1a1+a22+1a2+⋯+an2+1an≥2016. \dfrac{a_{1}^2+1}{a_{1}}+\dfrac{a_{2}^2+1}{a_{2}}+\cdots +\dfrac{a_{n}^2+1}{a_{n}} \geq 2016.a1a12+1+a2a22+1+⋯+anan2+1≥2016.
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