PE 66 Diophantine equation（Pell方程）

Diophantine equation

Problem 66

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.

题解：

​​http://oeis.org/A033316​​

​​http://mathworld.wolfram.com/PellEquation.html​​

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