Question

[QuangMinh Trần]

Tim cac so nguyen m,n,p thoa man p = m - n = m . n

Giup minh voi minh dang can gap

Answer 1

[Nguyễn Văn Hạ]

Ta có : \(m-n=mn\)

\(\Leftrightarrow mn-m+n=0\)

\(\Leftrightarrow m\left(n-1\right)+n-1=-1\)

\(\Leftrightarrow\left(m+1\right)\left(n-1\right)=-1\)\(\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}m+1=-1\\n-1=1\end{cases}}\\\hept{\begin{cases}m+1=1\\n-1=-1\end{cases}}\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}m+1=-1\\n-1=1\end{cases}}\\\hept{\begin{cases}m+1=1\\n-1=-1\end{cases}}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}m+1=1\\n-1=-1\end{cases}}\\\hept{\begin{cases}m+1=-1\\n-1=1\end{cases}}\end{cases}}\)