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The value of \left\{\frac{3^{2003}}{28}\right\}, where \{\cdot\} denotes the fractional part, is equal to

Option: 1

\frac{15}{28}


Option: 2

\frac{5}{28}


Option: 3

\frac{19}{28}


Option: 4

\frac{9}{28}


Answers (1)

best_answer

\begin{aligned} & 3^{2003}=3^{2001} \cdot 3^2=9(27)^{667}=9(28-1)^{667} \\ & =9\left({ }^{667} C_0 28^{667}-{ }^{667} C_1(28)^{666}+\ldots+{ }^{667} C_{667}(-1)^{667}\right) \end{aligned}

that means if we divide 3^{2003} by 28 , remainder is 19.
Thus, \left\{\frac{3^{2003}}{28}\right\}=\frac{19}{28}.

Posted by

Rishi

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