$2^9 + 2^{99}$
$= 2^9 + (2^{11})^9 \quad \vdots \quad 2 + 2^{11}$
$\to 2^9 + 2^{99} \quad \vdots \quad 2050$
$\to 2^9 + 2^{99}\quad \vdots \quad 50\quad (1)$
Ta lại có:
$2^9 + 2^{99}\quad \vdots \quad 2 + 2^{11}$
$\to 2^9 + 2^{99} = (2 + 2^{11})(2^8 - 2^7.2^{11} +\dots -2.2^{77} + 2^{88})$
Dễ dàng nhận thấy:
$2^8 - 2^7.2^{11} +\dots -2.2^{77} + 2^{88} \quad \vdots \quad 2\quad (2)$
$(1)(2)\Rightarrow 2^9 + 2^{99}\quad \vdots \quad 100$
