AMC 12 2003b Problem 24

Positive integers $a,b,$ and $c$ are chosen so that $a<b<c$, and the system of equations

$\mathrm{(A)}\ 668 \mathrm{(B)}\ 669 \mathrm{(C)}\ 1002 \mathrm{(D)}\ 2003 \mathrm{(E)}\ 2004$