Giải thích các bước giải:
+Nếu n chẵn
$\rightarrow n=2k(k\in N*)$
$\rightarrow 19.8^{2k}+17=18.8^{2k}+\left(1+63\right)^k+\left(18-1\right)\equiv 0(mod 3)$
$\rightarrow 19.8^{2k}+17\quad\vdots\quad 3$
+Nếu n lẻ
$Xét\quad n=4k+1$
$\rightarrow 19.8^{4k+1}+17=13.8^{4k+1}+6.8.64^{2k}+17$
$=13.8^{4k+1}+39.64^{2k}+9\left(1-65\right)^{2k}+\left(13+4\right)\equiv0(mod 13)$
$\rightarrow 19.8^{4k+1}+17\quad\vdots\quad 13$
$\text{Hoặc } n=4k+3$
$\rightarrow 19.8^{4k+3}+17=15.8^{4k+3}+4.8^3.64^{2k}+17=15.8^{4k+3}+4.510.64^{2k}+4.2\left(1-65\right)^{2k}+\left(25-8\right)\equiv0(mod 5)$
$\rightarrow 19.8^{4k+3}+17\quad\vdots\quad 5$
$\rightarrow 19.8^n+17$ là hợp số
