Find the remainder when 2256 is divided by 17.

Answer: Option A

$$\begin{array}{rl}& \text{Given},\\ & \frac{2^{256}}{17}\\ & \text{We}\text{can}\text{write}\text{it}\text{as}:{\left(2^4\right)}^{64}\\ & \frac{{16}^{64}}{17}\\ & \text{Individually, when 16 is divided by 17,}\\ & \text{gives a negative reminder of - 1}\text{.}\\ & \text{Required Remainder},\\ & {\left(-1\right)}^{64}=1\\ & \text{Alternatively},\\ & \frac{{16}^{64}}{17},\text{can}\text{be}\text{written}\text{as}\\ & \frac{\left(16\times 16\times 16\times 16\times 16......64\text{times}\right)}{17}\\ & \text{Now,}\text{we}\text{take}\text{the}\text{negative}\text{remainder}\text{of}\text{each,}\\ & \text{16}\text{divided}\text{by}\text{17}\text{gives}\text{negative}\text{remainder}\text{ - 1}\text{.}\\ & \text{So,}\text{the}\text{Remainder}\text{will}\text{be}\\ & \left(-1\times -1\times -1\times -1\times -1.......64\text{times}\right)\\ & =1\end{array}$$