GIVEN:
323^{13} + 527^{17}
CONCEPT:
Unit digit
FORMULA USED:
Cyclicity table:
Numbers |
Cyclicity |
1, 5, 6 |
1 |
4, 9 |
2 |
2, 3, 7, 8 |
4 |
CALCULATION:
Unit digit of 323^{13} = Unit digit of 3^{13} = Unit digit of (3^{4})^{3} × 3^{1}
Unit digit of (3^{4})^{3} is 1 and unit digit of 3^{1} is 3
Unit digit of 323^{13} = 1 × 3 = 3
Unit digit of 527^{17} = Unit digit of 7^{17} = Unit digit of (7^{4})^{34} × 7^{1}
Unit digit of (7^{4})^{4} is 1 and unit digit of 7^{1} is 7
Unit digit of 527^{17} = 1 × 7 = 7
Hence,
Sum = 3 + 7 = 10
∴ Required unit digit = 0