Question

find the remainder when 59power 28 is divided by 7

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ \mathrm{Remainder}\mathrm{of}\frac{{59}^{28}}{7} \\ =\mathrm{Remainder}\mathrm{of}\frac{{\left(56+3\right)}^{28}}{7} \\ =\mathrm{Remainder}\mathrm{of}\frac{3^{28}}{7}=\mathrm{Remainder}\mathrm{of}\frac{{\left(3^2\right)}^{14}}{7} \\ =\mathrm{Remainder}\mathrm{of}\frac{{\left(7+2\right)}^{14}}{7}=\mathrm{Remainder}\mathrm{of}\frac{2^{14}}{7} \\ =\mathrm{Remainder}\mathrm{of}\frac{{\left(2^3\right)}^4\times 2^2}{7}=\mathrm{Remainder}\mathrm{of}\frac{{\left(7+1\right)}^4\times 2^2}{7} \\ =1\times 4 \\ =4 \end{gathered}$$