negative pell's equation If $d$ is divisible by a prime $p \equiv 3 \pmod{4}$. show that the equation $x^2-dy^2=-1$ has no solution. So far I have learn only positive Pell's equation but not negative Pell's equation. We know that in positive Pell's equation, it always has a solution but not the case for negative Pell's equation. Can anyone give some hints on how to tackle this question?

Suppose a solution exists. Then reducing mod $p$ we find that $x^2 \equiv -1 \bmod p$. Then $\left(\frac{-1}{p}\right) = 1$. However $p\equiv 3 \bmod 4$ so this is a contradiction.