2013 Gauss 8 Problem 15

When 10\,000 is divided by 13, the remainder is 3. Which one of the following numbers also gives a remainder of 3 when divided by 13?

\textbf{(A)}\ 9997\quad \textbf{(B)}\ 10\,003\quad \textbf{(C)}\ 10\,013\quad \textbf{(D)}\ 10\,010\quad \textbf{(E)}\ 10\,016

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.