Question

The remainder left out when $8^{2n}-(62{)}^{2n+1}$ is divided by $9$ is

• A. $0$
• B. $2$
• C. $7$
• D. $8$

Answer 1

The correct option is B $2$

$8^{2n}-(62{)}^{2n+1}$

$\Rightarrow (63+1{)}^n-(63-1{)}^{2n+1}$

$\Rightarrow (63+1{)}^n+(1-63{)}^{2n+1}$

$\Rightarrow \left(1{+}^n{C}_1\right(63).....)+\left(1{-}^{2n+1}{C}_1\right(63).......)$

$\Rightarrow 2+63{(}^n{C}_1{+}^n{C}_2\left(63\right).......)$

So, the remainder will be $2$

Hence, option 'B' is correct.