Problem:
A subset of the integers has the property that none of its members is times another. What is the largest number of members such a subset can have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For each positive integer that is not divisible by , we must decide which of the numbers in the list to place in the subset. Clearly, a maximal subset can be obtained by using alternate numbers from this list starting with . Thus, it will contain members that are not divisible by members that are divisible by but not by , and member divisible by , for a total of elements.
Note. The maximal subset is not unique. For example, for each between and that is not divisible by , either or could be used.