2013 AMC 10A Problems/Problem 19
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 digits
does the base-
-representation of
end in the digit
?
Solution
We want the integers such that
is a factor of
. Since
, it has
factors. Since
cannot equal
or
, our answer is