Giải thích các bước giải:
a.Ta có :
$A=2^{2000}-1=(2^4)^{500}-1=16^{500}-1\quad\vdots\quad 16-1=15\quad\vdots\quad 5$
b.$2x^2-2xy=5x+y-3$
$\rightarrow 2x^2-5x+3=2xy+y$
$\rightarrow 2x^2+x-6x-3+6=y(2x+1)$
$\rightarrow x(2x+1)-3(2x+1)+6=y(2x+1)$
$\rightarrow y=x-3+\dfrac{6}{2x+1}$
Để $y\in Z\rightarrow 2x+1\in U(6)=\{1,-1,3,-3\},2x+1$ lẻ
$\rightarrow x\in\{0,-1,1,-2\}$
$\rightarrow y\in\{3,-9.98,0, -7 \}$
$\Rightarrow (x,y)\in\{(0,3), (1,0), (-2,-7)\}$