Question

What is the remainder when 17to the power 5 is divided by 9.

Answer 1

Dear student
$$\begin{gathered} \mathrm{When}(\mathrm{a}+\mathrm{b}{)}^{\mathrm{n}}\mathrm{is}\mathrm{divided}\mathrm{by}\mathrm{a},\mathrm{remainder}\mathrm{is}{\mathrm{b}}^{\mathrm{n}} \\ \mathrm{So},\frac{{17}^5}{9}=\frac{{\left(18-1\right)}^5}{9} \\ \mathrm{Remainder}\mathrm{will}\mathrm{be}(-1{)}^{15}=-1 \\ \mathrm{So},-1+9=8\mathrm{is}\mathrm{the}\mathrm{final}\mathrm{remainder}. \\ \mathrm{Note}:\mathrm{When}\mathrm{remainder}\mathrm{is}\mathrm{negative}\mathrm{we}\mathrm{add}\mathrm{divisor}. \end{gathered}$$
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