\(2^x-2^y=64\)
\(\Rightarrow2^y\left(2^{x-y}-1\right)=64\)
Dễ thấy \(x\ne y\) và \(2^{x-y}⋮2\Rightarrow2^{x-y}-1\) chia \(2\) dư \(1\)
Mà \(64⋮2^{x-y}-1\) suy ra \(\left\{\begin{matrix}2^y=64\\2^{x-y}-1=1\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}y=6\\2^{x-y}=2\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}y=6\\x-y=1\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=7\\y=6\end{matrix}\right.\)
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