Câu 1:
Ta có: $2002\vdots 2\Rightarrow 2002^{2003}\vdots 2$
$2003\not\vdots 2\Rightarrow 2003^{2004}\not\vdots 2$
$\Rightarrow 2002^{2003}+2003^{2004}\not\vdots 2$
Câu 2:
$3^2\equiv -1\pmod 5$
$\Rightarrow 3^{4n}=(3^2)^{2n}\equiv (-1)^{2n}\equiv 1\pmod 5$
$\Rightarrow 3^{4n}-6\equiv 1-6\equiv 0\pmod 5$
$\Rightarrow 3^{4n}-6\vdots 5$
Câu 3:
$2001\equiv 1\pmod {10}$
$\Rightarrow 2001^{2002}\equiv 1^{2002}\equiv 1\pmod {10}$
$\Rightarrow 2001^{2002}-1\equiv 1-1\equiv 0\pmod {10}$
Vậy $2001^{2002}-1$ chia hết cho $10$