652 B
652 B
Consider quadratic Diophantine equations of the form:
x^2 – Dy^2 = 1
For example, when D=13, the minimal solution in x is 649^2 – 13×180^2 = 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:
3^2 – 2×2^2 = 1
2^2 – 3×1^2 = 1
9^2 – 5×4^2 = 1
5^2 – 6×2^2 = 1
8^2 – 7×3^2 = 1
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.