Question

2012^2012+2018^2018+2019^2019последняя цифра решенного примера​

Answer 1

Ответ:

9  , последняя цифра числа - остаток при делении этого числа  на 10 ( комментарий к второму варианту решения )

Пошаговое объяснение:

Answer 2

To find the last digit of the expression 2012^2012 + 2018^2018 + 2019^2019, we need to calculate each term and then add them together.

Let's start with the first term:

2012^2012

To find the last digit of a number raised to a power, we can use the concept of cyclicity. The last digit of 2012 is 2. For powers of 2, the last digit follows a cyclical pattern: 2, 4, 8, 6. Since 2012 is divisible by 4 (2012 = 503 * 4), the last digit of 2012^2012 will be the same as the last digit of 2^2012, which is 6 (2012 mod 4 = 0).

Next, let's move on to the second term:

2018^2018

The last digit of 2018 is 8. For powers of 8, the last digit follows a cyclical pattern: 8, 4, 2, 6. Since 2018 is divisible by 4 (2018 = 504 * 4 + 2), the last digit of 2018^2018 will be the same as the last digit of 8^2018, which is 6 (2018 mod 4 = 2).

Finally, let's calculate the last digit of the third term:

2019^2019

The last digit of 2019 is 9. For powers of 9, the last digit follows a cyclical pattern: 9, 1, 9, 1. Since 2019 is divisible by 2 (2019 = 1009 * 2 + 1), the last digit of 2019^2019 will be the same as the last digit of 9^2019, which is 9 (2019 mod 2 = 1).

Now, let's add the last digits of each term together:

6 + 6 + 9 = 21

The last digit of the expression 2012^2012 + 2018^2018 + 2019^2019 is 1.