Find all the quadruples [a, b, c, d] where a^3 + b^3 = c^3 + d^3 when 1 <= a, b, c or d <= 10000 [closed]

Answer 1

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Logic :
a^3 + b^3 = c^3 + d^3
Then, a^3+b^3-c*3-d^3 = 0
Try to solve this equation by putting all combination of values for a,b,c and d in range of [0 , 10^5].
If equation is solved print the values of a,b,c and d

public static void main(String[] args) {

        //find all solutions of a^3 + b^3 = c^3 + d^3
        double power = 3; 
        long counter = 0; // to count the number of solution sets obtained
        int limit = 100000; // range from 0 to limit

        //looping through every combination of a,b,c and d
        for(int a = 0;a<=limit;a++)
        {
            for(int b = 0;b<=limit;b++)
            {
                for(int c = 0;c<=limit;c++)
                {
                    for(int d = 0;d<=limit;d++)
                    {
                        // logic used : a^3 + b^3 = c^3 + d^3 can be written as a^3 + b^3 - c^3 - d^3 = 0
                        long result = (long)(Math.pow(a,power ) + Math.pow(b,power ) - Math.pow(c,power ) - Math.pow(d,power ));
                        if(result == 0 )
                        { 
                            counter++; // to count the number of solutions
                            //printing the solution
                            System.out.println( "a = "+ a + "    b = " + b + "    c = " + c + "    d = " + d);
                        }
                    }
                }
            }
        }
        //just to understand the change in number of solutions as limit and power changes

        System.out.println("Number of Solutions =" + counter);
    }