EularProject 66：Diophantine equation

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/zhangzhengyi03539/article/details/78447060

Andrew Zhang
Nov 4, 2017

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.

Answer:
661
Completed on Thu, 26 Oct 2017, 17:30
Go to the thread for problem 66 in the forum.