Mock AIME II 2012 Problems/Problem 1
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Problem
Given that where
and
are positive relatively prime integers, find the remainder when
is divided by
.
Solution
Consider . We note that
, thus we have a telescoping sequence and we need only consider the first numerator and last denominator.
Note that however
. Also, note that
however
. Since
, we know that
. Now note that we want
, therefore we use
and
to give us
.