Problem:
Let be the set of positive integers for which has the repeating decimal representation , with and different digits. What is the sum of the elements of ?
Answer Choices:
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Solution:
If satisfies the equation , then and subtracting gives . The positive factors of 99 are , and 99. Only , and 99 give a number consisting of two different digits, namely 09,03 , and 01 , respectively. Thus the requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions