Question

[Hoàng Thúy An]

tim cac so m,n nguyen duong la a

\(2^m-2^n=256\)

Answer 1

[Võ Thành Đạt]

\(2^m-2^n=256\)

\(\Rightarrow2^n\left(2^{m-n}-1\right)=256\)

Vì \((2^{m-n}-1)\)không chia hết cho 2

Mà \(\)256 chia hết cho \(2^{m-n}-1\)

Nên \(2^{m-n}-1=1\)

\(\Rightarrow2^{m-n}=1+1=2\)

\(\Rightarrow m-n=1\)

\(\Rightarrow2^n\left(2^1-1\right)=256\)

\(\Rightarrow2^n=2^8\)

\(\Rightarrow n=8\\\)

\(\Rightarrow m=8+1=9\)

Vậy m=9,n=8