2006 AIME A Problems/Problem 3
Problem
Find the least positive integer such that when its leftmost digit is deleted, the resulting integer is 1/29 of the original integer.
Solution
The number can be represented as , where
is the leftmost digit, and
is the rest of the number. We know that
. Thus
has to be 7 since
can not have 7 as a factor, and the smallest
can be and have a factor of
is
We find that
is 25, so the number is 725.