# Problem 66: Diophantine equation

![graphic](img066.gif)

Consider quadratic Diophantine equations of the form: x2 – Dy2 = 1 For
example, when D=13, the minimal solution in x is 6492 – 13×1802 = 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: 32 – 2×22 = 1 22 – 3×12 = 192 – 5×42 = 1 52 – 6×22
= 1 82 – 7×32 = 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.