Problem:
What is the units digit of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Powers of have the same units digit as the corresponding powers of ; and
Since the units digit of is the same as the units digit of , units digits of powers of cycle through , and . Hence the units digit of is , so the units digit of is . The same is true of the units digit of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions