Question

If {x} denotes the fractional part of x then the value of $\left\{\frac{2^{2003}}{17}\right\}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$2^{2003}=(2^4{)}^{500}.2^3=8(16{)}^{500}$

= 8 $(17-1{)}^{500}$

= 8 $[{17}^{500}-{}^{500}{C}_1(17{)}^{499}+......-{}^{500}{C}_{499}\left(17\right)+1]$

$\frac{2^{2003}}{17}=8K+\frac{8}{17}$

$\Rightarrow$ $\left\{\frac{2^{2003}}{17}\right\}=\frac{8}{17}$