What is the remainder when $_{20} 51^{97}$ is divided by 17?

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 10
$\frac{20^{51^{27}}}{17} \Rightarrow \frac{3^{51^{97}}}{17} \Rightarrow \frac{51^{97}}{16}$ [Since 17 is a prime number]
$\Rightarrow \frac{3^{97}}{16} \Rightarrow \frac{3. (80 + 1)^{24}}{16} \Rightarrow \frac{3^{3}}{17} \Rightarrow$ 10 as the remainder

Suggest Corrections

Similar questions

30^{40}

13^{17} + 17^{13}

_{55} 56^{57}

17^{200}

18

2^{256}

17

Join BYJU'S Learning Program