Problem 29

问题描述：

Consider all integer combinations of a^b for 2 a 5 and 2 b 5:

2 ²=4, 2 ³=8, 2 ⁴=16, 2 ⁵=32
3 ²=9, 3 ³=27, 3 ⁴=81, 3 ⁵=243
4 ²=16, 4 ³=64, 4 ⁴=256, 4 ⁵=1024
5 ²=25, 5 ³=125, 5 ⁴=625, 5 ⁵=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 a^b for 2 a 100 and 2 b 100?

解决问题：

java里有set，每次计算出来，都将值放入其中，然后统计。

public static int count(){
		int total = 0;
		Set<Double> all = new HashSet<Double>();
		
		for(int i=DOWN; i<=UP; i++){
			for(int j=DOWN; j<=UP; j++){
				double value = Math.pow(i, j);
				all.add(value);
			}
		}
		
		return all.size();
	}