no Integer solutions to $X^2-nY^2=-1$ $n=3 \pmod 4$ a Natural number, prove there are no Integer solutions to $X^2-nY^2=-1$
I don't really know how to start this one...a little help?

HINT: the only squares modulo $4$ are $\bar 0$ and $\bar 1$. On the other hand the equation $X^2-nY^2=-1$ reduces modulo $4$ to
$$
X^2+Y^2=\bar 3
$$
since $\bar n=\overline{-1}$.
Thus ....
