Find the remainder if $30^{40}$ 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 1
$\frac{30^{40}}{17} = \frac{(34 - 4)^{40}}{17} = \frac{(- 4)^{40}}{17} = \frac{4^{40}}{17}$
$= \frac{(4^{2})^{20}}{17} = \frac{16^{20}}{17}$
$= \frac{(17 - 1)^{20}}{17} = \frac{(- 1)^{20}}{17} = \frac{1}{17}$
So, the required remainder is 1.

Suggest Corrections

Similar questions

30^{40}

200^{1000}

Find the remainder when $128^{129}$ is divided by 17.

Join BYJU'S Learning Program