Project Euler > Problem 29 > Distinct powers (Java Solution)

Problem:

Consider all integer combinations of ab for 2 [≤] a [≤] 5 and 2 [≤] b [≤] 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 [≤] a [≤] 100 and 2 [≤] b [≤] 100?

Solution:

9183

Code:
The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 29
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */

import java.math.BigInteger;
import java.util.HashSet;
import java.util.Set;


public final class p029 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p029().run());
 }
 
 
 public String run() {
  Set<BigInteger> generated = new HashSet<BigInteger>();
  for (int a = 2; a <= 100; a++) {
   for (int b = 2; b <= 100; b++)
    generated.add(BigInteger.valueOf(a).pow(b));
  }
  return Integer.toString(generated.size());
 }
 
}