Equation - Diophantine Equations

SOURCE:COMPETITION
Number of Problems: 5. : (Book)

1.

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Let $a$ , $b$ , and $c$ be positive integers with $age$ $bge$ $c$ such that $a^2-b^2-c^2+ab=2011$ and $a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$ .

What is $a$ ?

$extbf{(A)} 249qquad extbf{(B)} 250qquad extbf{(C)} 251qquad extbf{(D)} 252qquad extbf{(E)} 253$

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5.