$\left\{\begin{array}{l} mx+2y=m+1\\ 2x+my=2m-1\end{array}\right.\\ \Leftrightarrow \left\{\begin{array}{l} 2mx+4y=2m+2\\ 2mx+m^2y=2m^2-m\end{array}\right.\\ \Leftrightarrow \left\{\begin{array}{l} 2mx+4y=2m+2\\ (m^2-4)y=2m^2-3m-2\end{array}\right.\\ \Leftrightarrow \left\{\begin{array}{l} 2mx+4y=2m+2\\ (m-2)(m+2)y=(2m+1)(m-2)\end{array}\right.\\ \Leftrightarrow \left\{\begin{array}{l} 2mx+4y=2m+2\\ (m+2)y=2m+1\end{array}\right.(*)\\ \circledast m=-2 (*)\Leftrightarrow \left\{\begin{array}{l} 2mx+4y=2m+2\\ 0=-3\end{array}\right.(L)\\ \circledast m\ne-2 (*)\Leftrightarrow \left\{\begin{array}{l} x=\dfrac{m-1}{m+2}\\ y=\dfrac{2m+1}{m+2}\end{array}\right.\Leftrightarrow \left\{\begin{array}{l} x=1-\dfrac{3}{m+2}\\ y=2-\dfrac{3}{m+2}\end{array}\right.$ Pt có nghiệm nguyên $\Rightarrow (m+2)\in Ư(3)$ $\Rightarrow m\in\{1;-5;-1-3\}$
Kết hợp yêu cầu đề $\Rightarrow m\in\{-5;-1-3\}$
