Find the remainder when 2²⁵⁶ is divided by 17.
a) 1
b) 16
c) 14
d) None of these

Answer: a
Explanation:
$$\eqalign{ & \frac{{{2^{256}}}}{{17}} \cr & {\text{We}}\,{\text{can}}\,{\text{write}}\,{\text{it}}\,{\text{as}}:\,{\left( {{2^4}} \right)^{64}} \cr & \frac{{{{16}^{64}}}}{{17}} \cr & {\text{Individually, when 16 is divided by 17,}} \cr & {\text{gives a negative reminder of – 1}}{\text{.}} \cr & {\text{Required Remainder}}, \cr & {\left( { – 1} \right)^{64}} = 1 \cr} $$