# Problem #1069

 1069 What is the largest integer that is a divisor of $$(n+1)(n+3)(n+5)(n+7)(n+9)$$ for all positive even integers $n$? $\textbf{(A) } 3 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 11 \qquad\textbf{(D) } 15 \qquad\textbf{(E) } 165$ This problem is copyrighted by the American Mathematics Competitions.
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