Ramanujan Numbers

 

Write a Java program to find any number between 1 and n that can be expressed as the sum of two cubes in two (or more) different ways.

Here are some examples of Ramanujan numbers :
1729 = 1^3 + 12^3 = 9^3 + 10^3
* 10000
1729 = 1^3 + 12^3 = 9^3 + 10^3
4104 = 2^3 + 16^3 = 9^3 + 15^3
* 100000
1729 = 1^3 + 12^3 = 9^3 + 10^3
4104 = 2^3 + 16^3 = 9^3 + 15^3
13832 = 2^3 + 24^3 = 18^3 + 20^3
39312 = 2^3 + 34^3 = 15^3 + 33^3
46683 = 3^3 + 36^3 = 27^3 + 30^3
32832 = 4^3 + 32^3 = 18^3 + 30^3
40033 = 9^3 + 34^3 = 16^3 + 33^3
20683 = 10^3 + 27^3 = 19^3 + 24^3
65728 = 12^3 + 40^3 = 31^3 + 33^3
64232 = 17^3 + 39^3 = 26^3 + 36^3

Sample Solution:

Java Code:

import java.util.Scanner;
public class Example21  {

   public static void main(String[] args) { 

         int n = 100000;
        // for each a, b, c, d, check whether a^3 + b^3 = c^3 + d^3
        for (int a = 1; a <= n; a++) {
            int a3 = a*a*a;
            if (a3 > n) break;

            for (int b = a; b <= n; b++) {
                int b3 = b*b*b;
                if (a3 + b3 > n) break;

                 for (int c = a + 1; c <= n; c++) {
                    int c3 = c*c*c;
                    if (c3 > a3 + b3) break;

                    for (int d = c; d <= n; d++) {
                        int d3 = d*d*d;
                        if (c3 + d3 > a3 + b3) break;

                        if (c3 + d3 == a3 + b3) {
                            System.out.print((a3+b3) + " = ");
                            System.out.print(a + "^3 + " + b + "^3 = "); 
                            System.out.print(c + "^3 + " + d + "^3"); 
                            System.out.println();
                        }
                    }
                }
            }
        }
    }
}

Sample Output:

1729 = 1^3 + 12^3 = 9^3 + 10^3                                                                                
4104 = 2^3 + 16^3 = 9^3 + 15^3                                                                                
13832 = 2^3 + 24^3 = 18^3 + 20^3                                                                              
39312 = 2^3 + 34^3 = 15^3 + 33^3                                                                              
46683 = 3^3 + 36^3 = 27^3 + 30^3                                                                              
32832 = 4^3 + 32^3 = 18^3 + 30^3                                                                              
40033 = 9^3 + 34^3 = 16^3 + 33^3                                                                              
20683 = 10^3 + 27^3 = 19^3 + 24^3                                                                             
65728 = 12^3 + 40^3 = 31^3 + 33^3                                                                             
64232 = 17^3 + 39^3 = 26^3 + 36^3