# Functions Problem 2

Did you actually have a solution worked out? Or were you just
frustrated and want to give up and peek? Here's a really
big hint. See if that helps any.

### Big hint

There are 2049 natural numbers \(\le 2048\).
So there are 2049 numbers of the form \(13^m\).
However, there are only 2013 remainders when you
divide numbers by 2013.
Notice that 2013 is smaller than 2049.

Ok, so how about representing each value
\(13^m\) using its quotient and remainder when divided
by 2013. That is \(13^m = q_m2013 + r_m\).

### And then ...

How long since you had a meal? Too long. Go get food. Is it
2am. Go to bed. You can't do math when you are hungry or
tired, especially this kind of problem.

If it's 2am before the Tuesday examlet, GO TO BED. Margaret said
in lecture that this kind of evil trick question won't be on the
examlets. Wait until after the examlet and give it another try.

Once you've tried all that, and either have a solution or are really
stuck permanently,
then look at the solution.