Problem:
When is divided by , the remainder is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since any positive integer(expressed in base ten) is some multiple of plus its last digit, its remainder when divided by can be obtained by knowing its last digit.
Note that ends in ends in ends in ends in , and this alternation of and endings continues with all even powers ending in . Therefore, the remainder when is divided by is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions