Question

Find the remainder when 7^98 is divided by 5

Answer 1

u can use binomial theorm here
\(\large\tt \begin{align} \color{black}{Rem~~\dfrac{7^{98 }}{5}\\~\\
Rem~~\implies \dfrac{(5+2)^{98 }}{5}\\~\\
Rem~~\implies \dfrac{(2)^{98 }}{5}\\~\\
Rem~~\implies \dfrac{(4)^{49 }}{5}\\~\\
Rem~~\implies \dfrac{(5-1)^{49 }}{5}\\~\\
Rem~~\implies \dfrac{(-1)^{49 }}{5}\\~\\
Rem~~\implies \dfrac{(-1)}{5}\\~\\
Rem~~\implies \huge 4\\~\\
}\end{align}\)