A simple function

Algebra Level 5

Define a function \(f:Z\rightarrow Z\) such that \(f(x)={ x }^{ 2 }+x+1\) for every integer x. Find the largest positive integer "n" such that:

\( 2015\times f({ 1 }^{ 2 })\times f({ 2 }^{ 2 })⋯f({ n }^{ 2 })\quad ≥\quad { (f(1).f(2)⋯f(n)) }^{ 2 }\).

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