# Euler Problem 29

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?

Didn’t take long with ArrayLists and BigIntegers.

import java.util.*;
import java.math.*;

public class Euler29
{
public static void main(String[] args)
{
System.out.print(“Problem 29:\n”);
Euler29 e = new Euler29();
System.out.print(“Answer = ” + e.Problem()+ “\n”);
}
public String Problem ()
{
ArrayList<BigInteger> Combos = new ArrayList<BigInteger>();
for (int a = 2; a <= 100; a++)
{
for (int b = 2; b <= 100; b++)
{
BigInteger power = new BigInteger(String.valueOf(a));
power = power.pow(b);
if (Combos.contains(power) != true)