## Problem 29: Distinct powers

*Difficulty: Easy

Problem:

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?

How to solve:

Use Java (or any other programming languages that support big numbers)

Solution took 62 ms

I think that by mathematic analyze, we can point out how many duplicates numbers. For example, 100*100 is 10000, it means the maximum number of terms is 10000, but in 10000, there are possibly many numbers that are duplicated. Subtract 10000 from that, we got the answer. That will be way more faster than this, this is just merely brute force.

## Jim 11:20 am

onJuly 10, 2016 Permalink |I’ve been surfing on-line greater than 3 hours nowadays, but I never found any interesting article like yours.

It is pretty value sufficient for me. In my view, if all web owners and bloggers made excellent content as you

probably did, the web might be much more helpful than ever before. http://www.yahoo.net

## loctv 3:53 pm

onJuly 10, 2016 Permalink |Thank you for your compliment Jim.

It’s a great thing to hear people say that they like my posts, specifically, the content inside it.