Problem 5

Let $k=-d=m-2n>0$. Then $m/n=s^k$, so $n(s^k-2)=k$. For $k=1$, this forces $s=3,n=1$, giving $(a,b)=(27,3)$. For $k=2$, it forces $s=2,n=1$, giving $(a,b)=(16,2)$. For $k\ge3$, $2^k-2>k$, impossible.