I wrote this code to find the variables that will satisfy the diophantine equation (i.e. a^4 + b^4 + c^4 = d^4), for all variables belong to: (0 , 430000), and it takes forever to find the answer (I left the code running for two hours and got nothing). I know that this is caused by the algorithm or the approach I took, but I really couldn’t think of any better solution…

here’s the code:

#include <iostream> using namespace std; void main() {     //Here I use double because max value for int variables is too small for what I need.     double n = 0, LHS, RHS, valA, valB, valC, valD;          double *arrA, *arrB, *arrC, *arrD;     arrA = new double[430000]; //array to store all the powers of 4 for var A        arrB = new double[430000]; //array to store all the powers of 4 for var B     arrC = new double[430000]; //array to store all the powers of 4 for var C        arrD = new double[430000]; //array to store all the powers of 4 for var D     for (int count = 0; count < 430000; count++)     {         arrA[count] = n*n*n*n;               arrB[count] = n*n*n*n;               arrC[count] = n*n*n*n;         arrD[count] = n*n*n*n;               n++;         }         //this loop is a counter, it increments "b" by 1 when "a" reaches max value, and so on for each variable...     /*     N.B:      The variables that satisfy the equation should be the following:     a = 95800     b = 217519     c = 414560     d = 422481     Plug it in as initializers for the variables to check that the program is working fine.     */     int a = 0, b = 0, c = 0, d = 0;     while (d < 430000)     {                if (a == 430000)         {                        a = 0;              b++;                 }                if (b == 430000)          {                        a = 0;              b = 0;              c++;                 }                if (c == 430000)          {                        a = 0;              b = 0;              c = 0;              d++;                 }                        if (d == 430000)          {                        break;               }            LHS = arrA[a] + arrB[b] + arrC[c];               RHS = arrD[d];               if (LHS == RHS && (arrA[a] != arrB[b] != arrC[c] != arrD[d]))                {                        valA = a; valB = b; valC = c; valD = d;                      break;               }                a++;     }      if (d == 430000){         cout << "Couldn't find an answer! \n" }     else      {         cout << "value of A is:  " << valA << endl;         cout << "value of B is:  " << valB << endl;          cout << "value of C is:  " << valC << endl;          cout << "value of D is:  " << valD << endl;     } } 

If anyone could tell me how to speed up the code or could think of a better algorithm. There’s nothing wrong (IMO) in the code’s syntax or logic, but it is very very slow…

N.B: here’s a link to an article regarding the equation for further reading: https://www.jstor.org/stable/2008781?seq=1#page_scan_tab_contents

I’m using a 2013 macbook pro “running windows 10”, (intel i5 2.4GHz, 8GB RAM), MS Visual Studio 2017…