Problem:
The base-nine representation of the number is . What is the remainder when is divided by 5 ?
Answer Choices:
A.
B.
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E.
Solution:
Note that . Because even powers of 9 leave remainder 1 when divided by 5 and odd powers of 9 leave remainder congruent to -1 when divided by 5 , it follows that leaves remainder congruent to , so the requested remainder is .
The problems on this page are the property of the MAA's American Mathematics Competitions