17. Let $A$ and $B$ be two positive four-digit integers such that $A \times B=16^{5}+2^{10}$. Find the value of $A+B$.
17. Ans: 2049
$$
16^{5}+2^{10}=\left(2^{4}\right)^{5}+2^{10}=\left(2^{10}+1\right) 2^{10}=1025 \times 1024=41 \times 5^{2} \times 2^{10} .
$$

Without loss of generality, we may assume that $A \leq B$. It follows that $1000 \leq$ $A \leq 1024$, and a direct check shows that 1024 is the only number between 1000 and 1024 that divides $41 \times 5^{2} \times 2^{10}$. Thus, $A=1024$ and $B=1025$. Therefore,
$$
A+B=1024+1025=2049 \text {. }
$$