Problem:
In base , the number ends in the digit . In base , on the other hand, the same number is written as and ends in the digit . For how many positive integers does the base- representation of end in the digit ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For the base- representation of to end in the digit , the base must exceed . Also, must divide , so must be one of the positive integer factors of . Thus there are bases in which ends with a .
The problems on this page are the property of the MAA's American Mathematics Competitions