2014 AIME II Problems/Problem 7
Problem
Let . Find the sum of all positive integers
for which
Solution
Note that is
when
is odd and
when
is even. Also note that
for all
. Therefore
Because of this,
is a telescoping series of logs, and we have
Setting each of the above quantities to
and
and solving for
,
we get integer values of
and
so our desired answer is