Question

Aflati ultima cifra a nr:
A) 3^2019+5^2020+1^2021
B)2^2019+6^2020+2019^0
C) 4^2019+7^2020+8^2021_9^2022

Answer 1

Răspuns:

Explicație pas cu pas:

A)

3^1 se termina in 3

3^2 se termina in 9

3^3 se termina in 7

3^4 se termina in 1

3^5 se termina in 3

2019 : 4 = 504 rest 3

3^2019 se termina in 7

5 la orice putere se termina in 5

1 la orice putere = 1

numarul se termina in 7 + 5 + 1, adica in 3

______________

B)2^2019+6^2020+2019^0

2^1 se termina in 2

2^2  se termina in 4

2^3 se termina in 8

2^4 se termina in 6

2^5 se termina in 2

2019 : 4 = 504 rest 3

2^2019 se termina in 8

6 la orice putere se termina in 6

2019^0 = 1

Numarul se termina in 8 + 6 + 1, adica in 5

____________

C) 4^2019+7^2020+8^2021 - 9^2022

4^1 se termina in 4

4^2 se termina in 6

4^3 se termina in 4

2019 : 2  = 1009 rest 1

4^2019 se termina in 4

7^1 se termina in 7

7^2 se termina in 9

7^3 se termina in 3

7^4 se termina in 1

7^5 se termina in 7

2020 : 4 = 505 rest 0

7^2020 se termina in 1

8^1 se termina in 8

8^2 se termina in 4

8^3 se termina in 2

8^4 se termina in 6

8^5 se termina in 8

2021 : 4 = 505 rest 1

8^2021 se termina in 8

9^1 se termina in 9

9^2 se termina in 1

9^3 se termina in 9

2022 : 2 = 1011 rest 0

9^2022 se termina in 9

Numarul se termina in 4 + 1 + 8 - 9 , adica in 4