Mock AIME 1 2006-2007 Problems/Problem 3
Revision as of 15:48, 3 April 2012 by 1=2 (talk | contribs) (moved Mock AIME 1 2006-2007/Problem 3 to Mock AIME 1 2006-2007 Problems/Problem 3)
Let have
,
, and
. If
where
is an integer, find the remainder when
is divided by
.
Solution
By the Law of Cosines, . Since
is an angle in a triangle the only possibility is
. Since
we may apply Euler's totient theorem:
so
and so
and so
So the answer is