AMC10 2023 B

AMC10 2023 B · Q8

AMC10 2023 B · Q8. It mainly tests Remainders & modular arithmetic, Powers & residues.

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

$2022^{2023} + 2023^{2022}$ 的个位数是多少？

(A) 7 7

(B) 1 1

(D) 5 5

(E) 3 3

Answer

Correct choice: (A)

正确答案：（A）

Solution

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

$2022^{2023} + 2023^{2022} \equiv 2^3 + 3^2 \equiv 17 \equiv 7$ (mod 10)。$\boxed{\text{A}}$

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