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