Difference between revisions of "Mock AIME 4 2006-2007 Problems/Problem 7"
(Please check for rigor, improve if necessary,) |
|||
Line 34: | Line 34: | ||
*[[Mock AIME 4 2006-2007 Problems/Problem 6| Previous Problem]] | *[[Mock AIME 4 2006-2007 Problems/Problem 6| Previous Problem]] | ||
*[[Mock AIME 4 2006-2007 Problems]] | *[[Mock AIME 4 2006-2007 Problems]] | ||
+ | |||
+ | [[Category:Intermediate Number Theory Problems]] |
Revision as of 13:18, 13 February 2008
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
.