Problem:
Find the sum of all integer bases for which is a divisor of .
Solution:
We are asked to find all bases such that the base- number divides , and then to sum these bases. In base , and . The condition can be rewritten as , so must divide . Since the positive divisors of are , we set equal to each and find . Restricting to bases greater than leaves and , whose sum is . Therefore the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions