Difference between revisions of "2023 AMC 10B Problems/Problem 8"

Line 5: Line 5:
 
==Solution==
 
==Solution==
 
<math>2022^{2023} + 2023^{2022} \equiv 2^3 + 3^2 \equiv 17 \equiv 7</math> (mod 10). <math>\boxed{\text{B}}</math>
 
<math>2022^{2023} + 2023^{2022} \equiv 2^3 + 3^2 \equiv 17 \equiv 7</math> (mod 10). <math>\boxed{\text{B}}</math>
 +
~andliu766

Revision as of 15:26, 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). $\boxed{\text{B}}$ ~andliu766