# Euler Problem 29

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?

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)