Mock AIME 4 2006-2007 Problems/Problem 7
Problem
Find the remainder when is divided by 1000.
Solution
, so .
Therefore, we want .
Since , we want and .
, so .
Since , .
The only number that is and is . Therefore,
.
Since , we want to find and .
Since , .
And since , , , .
We have gotten somewhere.
The only number that satisfies and is .