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number theory intermediate

Problem

What is the units digit of

202 2^{2023} + 202 3^{2022}

?

(A)

7

(B)

1

(C)

9

(D)

5

Solution

202 2^{2023} + 202 3^{2022} \equiv 2^{3} + 3^{2} \equiv 17 \equiv 7

(mod 10).

7

Final answer

A