fozzzy wrote:
So if we are given a question what is the units digit of 777^{777}
we find the pattern for 7 (7,9,3,1)
then we divide \frac{777}{4} and the remainder is 1 so the units digit is 7^1 which is 7?
Is this correct?
we find the pattern for 7 (7,9,3,1)
then we divide \frac{777}{4} and the remainder is 1 so the units digit is 7^1 which is 7?
Is this correct?
Yes.
The units digit of 777^777 = the units digit of 7^777.
7^1 has the units digit of 7;
7^2 has the units digit of 9;
7^3 has the units digit of 3;
7^4 has the units digit of 1.
7^5 has the units digit of 7 AGAIN.
The units digit repeats in blocks of 4: {7, 9, 3, 1}...
The remainder of 777/4 is 1, thus the units digit would be the first number from the pattern, so 7.
Hope it's clear.