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 positive integers
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
, as these cannot have the digit 3 in their base representations, our answer is
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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