Consider quadratic Diophantine equations of the form: $$x^2-D{y}^2=1$$

For example, when $D=13$, the minimal solution in $x$ is ${649}^2-13\times {180}^2=1$.

It can be assumed that there are no solutions in positive integers when $D$ is square.

By finding minimal solutions in $x$ for $D=\{2,3,5,6,7\}$, we obtain the following:

$$\begin{array}{rl}{3}^2-2\times 2^2& =1\\ 2^2-3\times 1^2& =1\\ {\mathbf{9}}^2-5\times 4^2& =1\\ 5^2-6\times 2^2& =1\\ 8^2-7\times 3^2& =1\end{array}$$

Hence, by considering minimal solutions in $x$ for $D\le 7$, the largest $x$ is obtained when $D=5$.

Find the value of $D\le 1000$ in minimal solutions of $x$ for which the largest value of $x$ is obtained.