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 .
1 | public interface EulerSolution{ |
2 |
3 | public String run(); |
4 |
5 | } |
01 | /* |
02 | * Solution to Project Euler problem 29 |
03 | * By Nayuki Minase |
04 | * |
07 | */ |
08 |
09 | import java.math.BigInteger; |
10 | import java.util.HashSet; |
11 | import java.util.Set; |
12 |
13 |
14 | public final class p029 implements EulerSolution { |
15 | |
16 | public static void main(String[] args) { |
17 | System.out.println(new p029().run()); |
18 | } |
19 | |
20 | |
21 | public String run() { |
22 | Set<BigInteger> generated = new HashSet<BigInteger>(); |
23 | for (int a = 2; a <= 100; a++) { |
24 | for (int b = 2; b <= 100; b++) |
25 | generated.add(BigInteger.valueOf(a).pow(b)); |
26 | } |
27 | return Integer.toString(generated.size()); |
28 | } |
29 | |
30 | } |
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