Problem:
Let be a -digit number, and let and be the quotient and remainder, respectively, when is divided by . For how many values of is divisible by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that . Hence is divisible by if and only if is divisible by . Since , there are
such numbers.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions