2021 JMPSC Invitationals Problems/Problem 3
Problem
There are exactly even positive integers less than or equal to
that are divisible by
. What is the sum of all possible positive integer values of
?
Solution
must have exactly 5 even multiples less than
. We have two cases, either
is odd or even. If
is even, then
. We solve the inequality to find
, but since
must be an integer we have x = 18, 20. If
is odd, then we can set up the inequality
. Solving for the integers
must be
. The sum is
or