2022 AIME I Problems/Problem 12
Revision as of 23:59, 17 February 2022 by Oxymoronic15 (talk | contribs)
.= Problem ==
For any finite set , let
denote the number of elements in
. Define
where the sum is taken over all ordered pairs
such that
and
are subsets of
with
.
For example,
because the sum is taken over the pairs of subsets
giving
.
Let
, where
and
are relatively prime positive integers. Find the remainder when
is divided by
1000.