# Problem #1694

 1694 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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