Question

What is the remainder when ${}_{55}{56}^{57}$ is divided by 17?

• A. 1
• B. 4
• C. 13
• D. 17

Answer 1

The correct option is A 1

$\frac{{55}^{{56}^{57}}}{17}\Rightarrow \frac{(51+4{)}^{{56}^{57}}}{17}\Rightarrow \frac{4^{{56}^{57}}}{17}\Rightarrow \frac{(17-1{)}^{\{28\times {56}^{56}\}}}{17}$
$\frac{(17-1{)}^{evenpower}}{17}\Rightarrow$ 1 as the remainder