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2023 AMC 10B Problems/Problem 8

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What is the units digit of $2022^{2023} + 2023^{2022}$ ?

$\text{(A)}\ 7 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 3$

Solution

$2022^{2023} + 2023^{2022} \equiv 2^3 + 3^2 \equiv 17 \equiv 7$ (mod 10). $\boxed{\text{B}}$ ~andliu766

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