(a) Simplifying, we get $\frac{n-m}{mn}=\frac{1}{m-n}$, or $(n-m)(m-n)=mn$. Expanding gives $-m^2-n^2+2mn=mn$, or $m^2+n^2-mn=0$. The only integer solutions to this are $m=n=0$, which doesn't work in the original equation. Therefore, there are no solutions. $\blacksquare$ (b) Simplifying, we get $\frac{n-m}{mn}=\frac{1}{n-m}$, or $(n-m)^2=mn$. Expanding gives $n^2+m^2-2mn=mn$, or $m^2+n^2-3mn=0$. Once again, the only integer solutions are $m=n=0$, which doesn't work in the original equation. Therefore, there are no solutions. $\blacksquare$