Question

When $2^{256}$ is divided by $17$, the remainder would be:

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

Answer 1

The correct option is A $1$

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