# 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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