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Algebra Level 5

For all positive integers kk , define f(k)=k2+k+1f(k)=k^2+k+1 . Compute the largest positive integer nn such that 2015f(12)f(22)f(n2)(f(1)f(2)f(n))2.2015f(1^2)f(2^2)\cdots f(n^2)\geq \Big(f(1)f(2)\cdots f(n)\Big)^2.

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