Question 159
Show that if $m$ and $n$ are relatively prime positive integers, then
$$
\frac{n^4 + m}{m^2 + n^2} \quad \text{and} \quad \frac{n^4 - m}{m^2 - n^2}
$$
can not be integers simultaneously.
$$
\frac{n^4 + m}{m^2 + n^2} \quad \text{and} \quad \frac{n^4 - m}{m^2 - n^2}
$$
can not be integers simultaneously.