Question

Tìm STN m,n thỏa mãn: 2^m-2^n=2016

 

Answer 1

Vì \(2^m-2^n=2016\)

\(\Rightarrow2^m>2^n\Rightarrow m>n\Rightarrow m=p+n\)\(\Rightarrow2^m-2^n=2016\)

\(\Leftrightarrow2^{n+p}-2^n=2016\)

\(\Rightarrow2^n.2^p-2^n.1=2016\)

\(\Rightarrow2^n.\left(2^p-1\right)=2016\)

\(\orbr{\begin{cases}2^p-1⋮̸\\2016⋮32;2016⋮64̸\end{cases}}2\Rightarrow2^n=32\)

\(\Rightarrow n=5\Rightarrow2^m=2016+32=2048\)

\(\Rightarrow2^m=2^{11}\Rightarrow m=11\)

Vậy m=11;n=5

Answer 2

Tham khảo tại đây :  Câu hỏi của Nguyen Thi ngoc mai : https://olm.vn/hoi-dap/question/372192.html