Math New Drill (Level 3) : Remainder when the 100th power of 123 is divided by 11

Find the remainder when the number of the 100th power of 123 is divided by 11.

Noted 

Answer

The remainder is 1.

Solution

(123) ^100 = (11×11 + 2)^100

                     = (multiple of 11) + 2^100.

2^100 = (2^5)^20

            =(32)^20

            =｛11×3+(-1)｝^20= (multiple of 11) + (-1)^20

Thus, the answer is equal to the remainder that the 20th power of (-1) is divided by 11.

As (-1)^20=1, the answer is 1.