Question

When $2^{256}$ is divided by $17$, what will be the remainder?

• A. $1$
• B. $16$
• C. $14$
• D. None of these

Answer 1

Answer: (A)

$1$

When $2^{256}$ is divided by $17$ then,
$\Rightarrow \frac{2^{256}}{2^4+1}\Rightarrow \frac{(2^4{)}^{64}}{(2^4+1)}$
By remainder theorem when $f\left(x\right)$ is divided by $(x+a)$ the remainder $=f(-a)$
Here, $f\left(x\right)=(2^4{)}^{64}$ and $x=2^4$ & $a=1$
$\therefore$ Remainder $=f(-1)=(-1{)}^{64}=1$