题目66：考察丢番图方程x^2 − Dy^2 = 1

欧拉计划

Diophantine equation

Consider quadratic Diophantine equations of the form:



For example, when D=13, the minimal solution in x is

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:



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

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

题目：

考虑如下形式的二次丢番图方程：



例如当 D=13 时, x 的最小解是

可以认为当 D 时平方数时方程无正整数解。

通过寻找当 D = {2, 3, 5, 6, 7} 时 x 的最小解，我们得到：



因此对于 D ≤ 7, x 的最小解的最大值在 D=5 时取到。

找出 D ≤ 1000 中使得 x 的最小值取到最大的 D 的值。