Problem:
What is the units digit of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The units digit of a power of an integer is determined by the units digit of the integer; that is, the tens digit, hundreds digit, etc... of the integer have no effect on the units digit of the result. In this problem, the units digit of is the units digit of . Note that ends in ends in ends in , and, in general, the units digit of odd powers of is , whereas the units digit of even powers of is . Since both exponents are odd, the sum of their units digits is , the units digit of which is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions