Giải thích các bước giải:
Ta có :
$A=5^{3n+2}+2^{2n+3}$
$\to A=25.5^{3n}+8.2^{2n}$
$\to A=25.5^{3n}+8.4^{n}$
$\to A=22.5^{3n}+11.4^{n}+3.5^{3n}-3.4^n$
$\to A=22.5^{3n}+11.4^{n}+3(5^{3n}-4^n)$
$\to A=22.5^{3n}+11.4^{n}+3(125^{n}-4^n)$
Vì $22\quad\vdots\quad 11,11\quad\vdots\quad 11,125^n-4^n\quad\vdots\quad 124-4\quad\vdots\quad 11$
$\to A\quad\vdots\quad 11$
$\to 5^{3n+2}+2^{2n+3}\quad\vdots\quad 11$
