Mathematics - Quadratic Equation Question with Solution | TestHub

Suppose m is positive integer such that $n^2+96=m^2$ then

$(m-n)(m+n)=96$

As $m-n<m+n$ and $m-n,m+n$ both must be even

So, the only possibilities are

$$\begin{array}{rlr}& m-n=2,m+n=48:m-n=4,m+n=24& m-n=6,m+n=16:m-n=8,m+n=12\end{array}$$

So, the solutions of $(m,n)$ are $(25,23),(14,10),(11,5),(10,2)$