20. Given that $a$ is a positive real number, $b$ is a positive integer and $2 \leqslant b \leqslant 200$, then the number of pairs $(a, b)$ that satisfy $\left(\log _{b} a\right)^{2017}=\log _{b} a^{2017}$ is $(\quad)$.
(A) 198
(B) 199
(C) 398
(D) 399
(E) 597
20. E.

Let $x=\log _{b} a$. Then
$$
x^{2017}=2017 x \text {. }
$$

If $x \neq 0$, then
$$
x^{2016}=2017 \Rightarrow x= \pm 2017^{\frac{1}{2016}} \text {. }
$$

Thus, equation (1) has exactly three real roots:
$$
x=0,2017^{\frac{1}{2016}},-2017^{\frac{1}{2016}} \text {. }
$$

By $\log _{b} a=x$, i.e., $a=b^{x}$, for each $b$ there correspond three different $a$, hence, the number of different pairs $(a, b)$ is $199 \times 3=597$.