2019 Mock AMC 10B Problems/Problem 22
Problem
Let be the set of all possible remainders when
is divided by
, where
is a positive integer and
is the number of elements in
. The sum
can be expressed as
where
are positive integers and
and
are as small as possible. Find
.
Solution
for all integer
. Therefore,
. Since the sum of the elements in
is
, the answer is
.