# Math Help - distinct power definition

1. ## distinct power definition

I'm sure that this definition is somewhere in my brain, but I cannot currently figure it out.

What is a "distinct power?"

(please excuse me if I've posted in the wrong place.)

Thank you!

2. This isn't a term I'm familiar with and a quick Google search doesn't find many results. Where is this term used? Perhaps it just means "distinct" in the sense of unique and different from any other powers used in the problem.

3. ahh, maybe this is why i'm confused! Thanks for your initial comments, Jameson.
It is on a list of various math-related questions and trivia.
This particular question is "The largest integer that is not a sum of distinct powers."

Using your supposition, I think that virtually any number can be in and of itself a power (itself to the first power), and it would be possible to make any number a sum of other numbers using various methods (7 could be 3^1 and 2^2). I just don't know if there's another way to look at it.

4. That question still seems fragmented. Is there any other info you can give me?

5. Thanks for your continued attention, Jameson.

I know only that the answer will be between 1 and 31 (in combination with the other questions that I have) in addition to the actual stated question. I feel better, now that an external person does not find this clear either!

So to confirm, all i have is the question "The largest integer that is not a sum of distinct powers." and that it is between 1 and 31 (inclusive).

Thanks.

6. If I had to venture a guess, I would say that something such as $2^2 + 3^2$ would be considered as a sum of distinct powers, since although both numbers are raised to the second power, they are different numbers.