From USAMO 2015

Algebra Level 3

Solve in integers for \(x\):

\[\large {x^2+xy+y^2= \left(\frac{x+y}{3}+1\right)^3}\]

If you get \(x\) as a polynomial in \(n\), where \(n\) is any integer (say \(x(n)\)), then find the maximum value of \(x(2)\).

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