Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 3"
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− | *[[Mock AIME 1 2006-2007/Problem 2 | Previous Problem]] | + | *[[Mock AIME 1 2006-2007 Problems/Problem 2 | Previous Problem]] |
− | *[[Mock AIME 1 2006-2007/Problem 4 | Next Problem]] | + | *[[Mock AIME 1 2006-2007 Problems/Problem 4 | Next Problem]] |
*[[Mock AIME 1 2006-2007]] | *[[Mock AIME 1 2006-2007]] |
Latest revision as of 15:53, 3 April 2012
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