Problem:
What is the units digit of ?
Answer Choices:
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Solution:
The units digit of is the same as the units digit of . The units digit of the powers of 2 cycle: Because 2023 has remainder 3 when divided by 4 , the units digit of is 8 . Similarly, the units digit of is the same as the units digit of . The units digit of the powers of 3 cycle: . Because 2022 has remainder 2 when divided by 4 , the units digit of is 9 . Thus the units digit of is the same as the units digit of , which is 7.
The problems on this page are the property of the MAA's American Mathematics Competitions