# Problem #1834

 1834 The product $(8)(888\ldots 8)$, where the second factor has $k$ digits, is an integer whose digits have a sum of $1000$. What is $k$? $\textbf{(A) }901\qquad \textbf{(B) }911\qquad \textbf{(C) }919\qquad \textbf{(D) }991\qquad \textbf{(E) }999\qquad$ This problem is copyrighted by the American Mathematics Competitions.
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