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2023 AMC 10B Problems/Problem 8: Difference between revisions

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What is the units digit of <math>2022^{2023} + 2023^{2022}</math>?


<math>\text{(A)}\ 7 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 3</math>
==Solution==
<math>2022^{2023} + 2023^{2022} \equiv 2^3 + 3^2 \equiv 17 \equiv 7</math> (mod 10). <math>\boxed{\text{B}}</math>

Revision as of 15:25, 15 November 2023

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). $\boxed{\text{B}}$

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