A4. How many pairs $(a, b)$ of positive integers with $a+b<100$ satisfy the equation: $a+\frac{1}{b}=13 \times\left(b+\frac{1}{a}\right)$?
(A) 5
(B) 7
(C) 9
(D) 13
(E) 28
A4. $\frac{a b+1}{b}=13 \times \frac{b a+1}{a}$. Thus $a=13 b$ and hence the seven pairs $(13,1),(26,2), \cdots,(91,7)$. (B)