Problem:
Let . What is the units digit of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The units digit of is , and 6 for , and 4 , respectively. For , the units digit of is equal to that of . Thus for every positive integer the units digit of is 6 , and hence has a units digit of 6 . The units digit of is 4 . Therefore the units digit of is 0 , so the units digit of is also 0 . Because 2008 is even, both and are multiples of 4 . Therefore is a multiple of 4 , so the units digit of is 6 , and the units digit of is also .
The problems on this page are the property of the MAA's American Mathematics Competitions