Question

What is the remainder when ${17}^{200}$ is divided by $18$?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$\Rightarrow$ When $n$ is even. $(x^n-a^n)$ is completely divisible by $(x+a)$

$\Rightarrow$ $({17}^{200}-1^{200})$ is completely divisible by $(17+1)$, i.e.,$18.$

$\Rightarrow$ $({17}^{200}-1)$ is completely divisible by $18$.

$\Rightarrow$ On dividing ${17}^{200}$ by $18$, we get $1$ as remainder.