Problem:
For which of the following integers is the base- number not divisible by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that
.
This number is divisible by if and only if either or is divisible by . Because neither nor is divisible by , the base-eight number is not divisible by . For all the other given choices for , either or is divisible by .
The problems on this page are the property of the MAA's American Mathematics Competitions