Question

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

• A. 1
• B. 16
• C. 14
• D. 15

Answer 1

The correct option is A 1

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

$\frac{2^{256}}{17}$

$=\frac{\left(2^{256}\right)}{16+1}$

$=\frac{2^{256}}{2^4+1}$

$=\frac{(2^4{)}^{64}}{2^4+1}$

If we take $x=2^4$, then the above expression can be written as

$\frac{x^{64}}{x+1}$

This implies division of $x^{64}$ by $x+1$

Remainder theorem states that when $f\left(x\right)$ is divided by $(x-a)$ the remainder obtained is $f\left(a\right)$

Thus, when $f\left(x\right)=x^{64}$ is divided by $x+1$, the remainder obtained is $f(-1)=(-1{)}^{64}$ which is 1.