Vì \(2^x-2^y=256>0\Rightarrow x>y\\ \)
\(\Rightarrow2^x-2^y=256\Leftrightarrow2^y.\left(2^{x-y}-1\right)=256\)
Vì \(x>y\Rightarrow x-y>0\Rightarrow2^{x-y}⋮2\Rightarrow2^{x-y}-1⋮̸2\)
Lại có: \(2^{x-y}-1\inƯ\left\{256\right\}\Rightarrow2^{x-y}-1\in\left\{\pm1\right\}\)
Nếu \(2^{x-y}-1=1\Rightarrow2^{x-y}=2\Leftrightarrow x-y=1\Leftrightarrow x=y+1\)và \(2^y=256\Rightarrow y=8\Rightarrow x=9\)
Nếu \(2^{x-y}-1=-1\Rightarrow2^y=-256\Rightarrow y=\varnothing\)vì y thuộc Z
Vậy (x,y)=(9;8)
Đúng 0
Bình luận (0)