Question

The remainder when $100\times \left({99}^{10}\right)$ is divided by $(100\times 99)$ + 1 is

• A. 1
• B. 100
• C. 9900

Answer 1

The correct option is C 9900

Option (d)

Go from unitary method, try for smaller numbers. Consider 10x9${}^{10}$ = (10.9)9${}^9$

(10$\times$9)+1

Consider the remainder when $\frac{9^9}{91}$. go by frequency method.

$\frac{9^1}{91}{|}_R$=9

$\frac{9^2}{91}{|}_R$=-10

$\frac{9^3}{91}{|}_R$= -$\frac{90}{91}{|}_R$=+1

Therefore $\frac{9^9}{91}{|}_R$=1

Remainder will be only the first part of the numerator=10$\times$9, in the case we have considered = 90

And in the question = 100$\times$99= 9900