Question

Find the remainder when 4001000 is divided by 17?

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is B

1

This needs the application of basic remainder theorem, fermat theorem and frequency method

First find the remainder when 400 is divided by 17= 9

The problem changes to $\frac{9^{1000}}{17}$

From fermat theorem the Euler's number of 17 is 16.(for all prime numbers, euler's number=N-1)

1000 = 16k +8

Problem now changes to $\frac{9^8}{17}$

Going by frequency method . $\frac{9^4}{17}$ gives remainder -1 so $\frac{9^8}{17}$ will give remainder 1.