# Problem #2277

 2277 Let $a$, $b$, and $c$ be positive integers with $a\ge$ $b\ge$ $c$ such that \begin{align*}a^2-b^2-c^2+ab&=2011\text{ and}\\ a^2+3b^2+3c^2-3ab-2ac-2bc&=-1997.\end{align*} What is $a$? $\textbf{(A)}\ 249\qquad\textbf{(B)}\ 250\qquad\textbf{(C)}\ 251\qquad\textbf{(D)}\ 252\qquad\textbf{(E)}\ 253$ This problem is copyrighted by the American Mathematics Competitions.
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