Turns out it's already posted, but with no discussion.

If $17|n$ then $n \not | 20^n \to n \not | 20^n+17k$ If $17 \not |n$ then $17k=a \pmod n$ has solution for every $a$ so exists such $k= (-20^n)*(17)^{-1} \pmod n$ that $n|20^n + 17k$ So answer is $2017-[\frac{2017}{17}]=1899$