jagy@phobeusjunior:~$  ./Pell_Target_Fundamental
  Automorphism matrix:
    3   4
    2   3
  Automorphism backwards:
    3   -4
    -2   3

  3^2 - 2 2^2 = 1

 w^2 - 2 v^2 = 119 =  7 17

Tue May 21 12:25:13 PDT 2019

w:  11  v:  1  SEED   KEEP +-
w:  13  v:  5  SEED   KEEP +-
w:  19  v:  11  SEED   BACK ONE STEP  13 ,  -5
w:  29  v:  19  SEED   BACK ONE STEP  11 ,  -1
w:  37  v:  25
w:  59  v:  41
w:  101  v:  71
w:  163  v:  115
w:  211  v:  149
w:  341  v:  241
w:  587  v:  415
w:  949  v:  671
w:  1229  v:  869
w:  1987  v:  1405
w:  3421  v:  2419
w:  5531  v:  3911
w:  7163  v:  5065
w:  11581  v:  8189
w:  19939  v:  14099
w:  32237  v:  22795
w:  41749  v:  29521
w:  67499  v:  47729
w:  116213  v:  82175
w:  187891  v:  132859
w:  243331  v:  172061
w:  393413  v:  278185
w:  677339  v:  478951
w:  1095109  v:  774359
w:  1418237  v:  1002845
w:  2292979  v:  1621381
w:  3947821  v:  2791531
w:  6382763  v:  4513295
w:  8266091  v:  5845009
w:  13364461  v:  9450101

Tue May 21 12:25:44 PDT 2019

 w^2 - 2 v^2 = 119 =  7 17

jagy@phobeusjunior:~$

#include <iostream>
#include <stdlib.h>
#include <fstream>
#include <strstream>
#include <list>
#include <set>
#include <math.h>
#include <iomanip>
#include <string>
#include <algorithm>
#include <iterator>
#include <time.h>
#include <gmp.h>
#include <gmpxx.h>
#include "form.h"

using namespace std;

//   g++  -o Pell_Target_Fundamental Pell_Target_Fundamental.cc  -lgmp -lgmpxx


//  ./Pell_Target_Fundamental


int main()
{


   mpz_class target, d, t,s;

  d = 2;


  t =  3  ;
  s =  2  ;


cout << "  Automorphism matrix:  " << endl;
cout << "    " << t << "   " << d * s << endl;
cout << "    " << s << "   " << t << endl;


cout << "  Automorphism backwards:  " << endl;
cout << "    " << t << "   " << -d * s << endl;
cout << "    " << -s << "   " << t << endl;

  target =  119  ;

  int time_limit_in_seconds = 31;

  if ( t * t - d * s * s != 1 ) cout << " not 1 " << endl;
  else
  {
  cout  << endl << "  " << t << "^2 - " << d << " " << s << "^2 = " <<  t * t - d * s * s << endl ;
  cout  << endl << " w^2 - " << d << " v^2 = " << target << " = " << mp_Factored(target) << endl << endl;
   system("date");
   cout << endl;
  int printcount = 0;
  for(mpz_class y = 0; printcount < 61 && clock() < time_limit_in_seconds * CLOCKS_PER_SEC && y <= 1000000000; y++){
    mpz_class n = target + d * y * y;
    if ( n > 0 && mp_SquareQ(n ) )
    {
      ++printcount;
      mpz_class x;
      x =  mp_Sqrt( n);

       cout << "w:  " << x << "  v:  " << y ;
            if ( t * x - d * s * y <= 0 || -s * x + t * y <= 0)
            {
             cout << "  SEED ";
             if ( target < 0 && x * s <= (t -1) * y ) cout <<  "  KEEP +- ";
             else  if ( target > 0 && x * s >= (t +1) * y ) cout <<  "  KEEP +- ";
             else cout << "  BACK ONE STEP  " << t * x - d * s * y << " ,  " << -s * x + t * y ;

            }


       cout << endl;
    } // square

  } // for y
   cout << endl;
   system("date");
    cout << endl  << " w^2 - " << d << " v^2 = " << target  << " = " << mp_Factored(target)  << endl << endl;

  } // else 1



    return 0 ;
}

//   g++  -o Pell_Target_Fundamental Pell_Target_Fundamental.cc  -lgmp -lgmpxx


//  ./Pell_Target_Fundamental