What is the remainder when the digit 111,111 up to 124 terms is divided by 271?
The basic concept employed in this solution is that 100,000 divided by 271 leaves remainder as 1. Hence all the terms having powers greater than 5 or multiples of 5 are giving only remainder as 1 multiplied by corresponding coefficients.
For example remainder when 10^11 is divided by 271 = 1*10 = 10, since 10^10 will give remainder as 1 only. This simplifies the problem. Refer attached image for full solution.