Vi \(2^m-2^n=2016\Rightarrow2^m>2^n\Rightarrow m>n\)
Dat m=n+x (x thuoc N*)ta co:
\(2^m-2^n=2016\)
\(2^{n+k}-2^n=2016\)
\(2^n.2^k-2^n=2016\)
\(2^n\left(2^k-1\right)=2016\)(1)
Vi \(2^k-1\)la so le \(\Rightarrow2^k-1\) khong chia het cho 2 ma 2016 chia het cho 32 ma khong chia het cho 64
\(\Rightarrow2^k=32\)
\(2^k=2^5\)
\(\Rightarrow k=5\)
Thay k=5 vao (1) ta co:
\(2^5\left(2^n-1\right)=2016\)
\(32\left(2^n-1\right)=2016\)
\(2^n-1=2016:32\)
\(2^n-1=63\)
\(2^n=63+1\)
\(2^n=64\)
\(2^n=2^6\)
\(\Rightarrow n=6\)
Voi n=6;k=5 thi \(m=6+5=11\)
Vay \(n=6;m=11\)
Tick cho minh nha
m=11
n=5
mày mà ko tick đừng có mà trách
ai tick cho Trần Xuân Quyết mk sẽ ko tick cho người đó nữa.