yasir9909 wrote:
\(286^1^0-52^1^2=n\)
Quantity A |
Quantity B |
The units digit of n |
0 |
A : Quantity A is greater
B : Quantity B is greater
C : Both quantities are equal
D : Answer Cannot be determined
Units digit have a Cyclicity which can be found for any number..
If you have an integer, only the units digit of any power to that number is dependent only on the units digit of the base... For example.. 23678^9 ..the units digit will depend on units digit of base 23678.
All number will surely repeat unit digits after every fourth, although few don't change at all and few have Cyclicity after two..
(1) Same units digit always..
1...1^2=1^3=1^4=1..
5....\(5^1=5....5^2=25....5^3=125\), thus 5 every time
6.....\(6^1=6...6^2=36.....6^3=216\), thus 6 every time
0....0 every time..
(2) Cyclicity after two..
4...\(4^1=4...4^2=16...4^3=64\), thus 4,6,4,6..
9....\(9^1=9....9^2=81....9^3=729\), thus 9,1,9,1..
(3) Cyclicity after 4..
2.....2,4,8,6,2,4..
3....3,9,7,1,3,9...
7....7,9,3,1,7,9...
8.....8,4,2,6,8,4,2...
Here we have \(286^1^0-52^1^2=n\)
286 means 6 and 6 will have 6 as units digit always..
52^(12)= means 2^(12)...2^(4*3) will have same Cyclicity as 2^4 hence 6..
So units digit of n will be 6-6=0..