PROJECT EULER #66

Link to Project Euler 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 x 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 x 2² = 1
2² – 3 x 1² = 1
9² – 5 x 4² = 1
5² – 6 x 2² = 1
8² – 7 x 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.

This was the synthesis of the two previous questions, with a bit of study at wolfram.com (here and here) and some pencil and paper walkthroughs it was do-able. I guess I've used 15 hours to do these three problems. Uncommenting the commented statements prints the [a₀;(a₁,a₂,....a_r,a_r+1)] series and the p_r / q_r or p_2r+1 / q_2r+1 (depending on the parity of the series) convergents for each number.

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
   class Program
   {
       static void Main()
       {
           //Problem 66
           DateTime start = DateTime.Now;
           //first the code from problem 64
           Dictionary<int, List<int>> numbers = new Dictionary<int, List<int>>();
           for (int number = 2; number <= 1000; number++)
           {
               bool repeat;
               int a = (int)Math.Sqrt(number);
               List<int> sequence = new List<int> { a };
               numbers.Add(number, sequence);
               int x = 1;
               do
               {
                   if (Math.Sqrt(number) - (int)Math.Sqrt(number) == 0) break;
                   int b = number - a * a;
                   int integerPart = x * ((int)Math.Sqrt(number) + a) / b;
                   numbers[number].Add(integerPart);
                   a = -(a - integerPart * (b / x));
                   x = (b / x);
                   repeat = integerPart == 2 * numbers[number][0] ? true : false;
               } while (!repeat);
           }
           //then the modified code from problem 65
           BigInt maxNumerator=0;
           int d = 0;
           for (int i = 2; i <= 1000; i++)
           {
               if (Math.Sqrt(i) - (int)Math.Sqrt(i)!=0)
               {
                   int r = numbers[i].Count-1;
                   BigInt numerator_2 = 0, numerator_1 = 1, numerator = 0;
                   BigInt denominator_2 = 1, denominator_1 = 0, denominator = 0;
                   //var sequence = numbers[i];
             
                   if ((r) % 2 != 0)//is odd
                   {
                       //Console.Write("r is even ");
                       //Console.Write("Sqrt " + i + ": [");
                       //Console.Write(sequence[0] + ";(");
                       //for (int j = 1; j < sequence.Count; j++)
                       //    if (j < sequence.Count - 1)
                       //        Console.Write(sequence[j] + ",");
                       //    else
                       //        Console.WriteLine(sequence[j] + ")]");
                       //Console.WriteLine();
                       for (int j = 0; j < numbers[i].Count; j++)
                       {
                           numerator = numbers[i][j] * numerator_1 + numerator_2;
                           numerator_2 = numerator_1;
                           numerator_1 = numerator;
                           denominator = numbers[i][j] * denominator_1 + denominator_2;
                           denominator_2 = denominator_1;
                           denominator_1 = denominator;
                       }
                       for (int j = 1; j < numbers[i].Count-1; j++)
                       {
                           numerator = numbers[i][j] * numerator_1 + numerator_2;
                           numerator_2 = numerator_1;
                           numerator_1 = numerator;
                           denominator = numbers[i][j] * denominator_1 + denominator_2;
                           denominator_2 = denominator_1;
                           denominator_1 = denominator;
                       }
                   }
                   else//is even
                   {
                       //Console.Write("r is odd");
                       //Console.Write("Sqrt " + i + ": [");
                       //Console.Write(sequence[0] + ";(");
                       //for (int j = 1; j < sequence.Count; j++)
                       //    if (j < sequence.Count - 1)
                       //        Console.Write(sequence[j] + ",");
                       //    else
                       //        Console.WriteLine(sequence[j] + ")]");
                       //Console.WriteLine();
                       for (int j = 0; j < numbers[i].Count-1; j++)
                       {
                           numerator = numbers[i][j] * numerator_1 + numerator_2;
                           numerator_2 = numerator_1;
                           numerator_1 = numerator;
                           denominator = numbers[i][j] * denominator_1 + denominator_2;
                           denominator_2 = denominator_1;
                           denominator_1 = denominator;
                       }
                   }
                   if (numerator > maxNumerator)
                   {
                       maxNumerator = numerator;
                       d = i;
                   }
                   //Console.WriteLine("x = " + numerator.ToString());
                   //Console.WriteLine("y = " + denominator.ToString());
                   //Console.WriteLine("-----------------------------------------");
               }
           }
           Console.WriteLine(d);
           TimeSpan time = DateTime.Now - start;
           Console.WriteLine("This took {0}", time);
           Console.ReadKey();
       }
   }
}