1. Given $a, b$ are integers, $\frac{127}{a}-\frac{16}{b}=1$. Then the maximum value of $b$ is . $\qquad$
Ni. 1.2016.
The original equation is transformed into $b=\frac{16 a}{127-a}=\frac{127 \times 16}{127-a}-16$.
When and only when $127-a=1$, $b$ reaches its maximum value, at this time, $b=127 \times 16-16=2016$.