Euler Problem 66

Euler Problem 66:Investigate the Diophantine equation x2 − Dy2 = 1.

Varijanta 1. Korištenjem Mathematica

Rješenje se može vrlo lako dobiti korištenjem Wolframove Mathematike:

```maxX = 0;
Dmin = 0;
For[d = 2, d <= 1000, d++,
If[Mod[Length[Divisors[d]], 2] == 1, Continue[]];
solX = x /.FindInstance[x^2 - d*y^2 == 1 && x > 0 && y > 0, {x, y},Integers][[1]];
If[solX > maxX, maxX = solX; Dmin = d]]; Dmin
```

Varijanta 2: C# Implementacija sa BigNumber strukturom:

```using System;
using System.Collections.Generic;
using System.Numerics;
namespace EulerProblem66
{
class Program
{
static void Main(string[] args)
{
BigInteger x = 0;
BigInteger maxx = 0;
int maxd = 0;
for (int d = 2; d <= 1000; d++)
{
if (d % Math.Sqrt(d) == 0)
continue;
List<long> c = ContinedFraction(d);
x = PellEq(c);
if (x > maxx)
{
maxx = x;
maxd = d;
}
}
Console.WriteLine(maxd);
///Kraj
Console.WriteLine("Pres any key to continue..");
Console.Read();
}
static long GCD(long a, long b)
{
long r = a % b;
if (r == 0)
return b;
else
return GCD(b, r);
}
static List<long> ContinedFraction(long d)
{
List<long> e = new List<long>();
long d2 = (long)Math.Sqrt(d);
long a = d2;
long p = 0;
long q = 1;
do
{
e.Add(a);
p = a * q - p;
q = (d - p * p) / q;
a = (p + d2) / q;
} while (q != 1);

e.Add(a);
return e;
}
static BigInteger PellEq(List<long> c)
{
int l = c.Count - 1;
int per = l % 2 == 0 ? l - 1 : 2 * l - 1;

BigInteger a = c[0];
BigInteger a1 = 1;
BigInteger b = 1;
BigInteger b1 = 0;
BigInteger t;

a = c[0];
b = c[0] * b + b1;
for (int i = 1; i <= per; i++)
{
t = a;
a = c[(i - 1) % l + 1] * a + a1;
a1 = t;
t = b;
b = c[(i - 1) % l + 1] * b + b1;
b1 = t;
}
return a;
}
}
}
```
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