## Task B-1.2.

With which digit does the number $2^{2022}+3^{2022}+7^{2022}$ end?
## Solution.

Powers of 2, starting from $2^{1}$, end with the digits $2,4,8,6$ and then repeat periodically.

Powers of 3, starting from $3^{1}$, end with the digits $3,9,7,1$ and then repeat periodically.

Powers of 7, starting from $7^{1}$, end with the digits $7,9,3,1$ and then repeat periodically.

To determine the last digit of the powers $2^{2022}$, $3^{2022}$, and $7^{2022}$, we will find the remainder when the exponent 2022 is divided by 4. Since 2022 : $4=505$ with a remainder of 2, it follows:

The number $2^{2022}$ ends with the same digit as the number $2^{2}$, which is the digit 4.

The number $3^{2022}$ ends with the same digit as the number $3^{2}$, which is the digit 9.

The number $7^{2022}$ ends with the same digit as the number $7^{2}$, which is the digit 9.

1 point

The sum $2^{2022}+3^{2022}+7^{2022}$ ends with the same digit as the number $4+9+9=22$, so the units digit of the number $2^{2022}+3^{2022}+7^{2022}$ is 2.