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
.