Consider quadratic diophantine equations of the form x2 - Dy2 = 1.
For example, when D = 13, the minimal solution in x is 6492 - 13x1802 = 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 - 2x22 = 1, 22 - 3x12 = 1, 92 - 5x42 = 1, 52 - 6x22 = 1, 82 - 7x32 = 1
Hence, by considering minimal solutions in x for D ≤ 7, the largest x is obtained when D = 5.
Find the value of D ≤ n in minimal solutions of x for which the largest value of x is obtained. Begin by entering a number.