# Problem #1372

 1372 How many pairs of positive integers $(a,b)$ are there such that $a$ and $b$ have no common factors greater than $1$ and $$\frac{a}{b} + \frac{14b}{9a}$$ is an integer? $\textbf{(A) } 4 \qquad\textbf{(B) } 6 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 12 \qquad\textbf{(E) } \text{infinitely many}$ This problem is copyrighted by the American Mathematics Competitions.
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