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3.2 Results on equations with varying degrees: **Table 1 demonstrates the results obtained** 
when the system was run for different Diophantine equations with varying values for the degrees. It shows that irrespective of reasonably large values for degrees and higher values of N, the system could give solutions within a smaller number of iterations. This points out that those large values of N do not affect the efficiency of the system. In addition, the comparatively lesser number of iterations only consumed for finding the solutions also validate the effectiveness of the system in finding solutions of Diophantine equations with larger value of N. 

| Sr.                                                |                             | Diophantine Equation   | Degree   |       |    |
|----------------------------------------------------|-----------------------------|------------------------|----------|-------|----|
| No                                                 | of                          |                        |          |       |    |
| equation                                           | Solution                    | Iterations             |          |       |    |
| Found                                              |                             |                        |          |       |    |
| 1                                                  | x1  2 + x2  2               | = 625                  | 2        | 24,7  | 29 |
| 2                                                  | x1  3 + x2  3 = 1008        | 3                      | 10, 2    | 10    |    |
| 3                                                  | x1  4 + x2  4 = 1921        | 4                      | 6, 5     | 9     |    |
| 4                                                  | x1  5 + x2  5 = 19932       | 5                      | 7, 5     | 10    |    |
| 5                                                  | x1  6 +x2  6                | = 47385                | 6        | 6, 3  | 7  |
| 6                                                  | x1  7 + x2  7 = 4799353     | 7                      | 9, 4     | 11    |    |
| 7                                                  | x1  8 + x2  8               | = 16777472             | 8        | 8, 2  | 8  |
| 8                                                  | x1  9 + x2  9               | = 1000019683           | 9        | 10, 3 | 11 |
| 9                                                  | x1  10 +x2  10 = 1356217073 | 10                     | 8, 7     | 13    |    |
| Table 1: Results on equations with varying degrees |                             |                        |          |       |    |

3.3 Results on equations with varying number of variables: **Table 2 shows the results** obtained when HILL-DOES was run on Diophantine equations with varying number of variables. This shows that the system provides solutions even when the number of variables is competitively high. 