Question

The remainder obtained when 100*(99${}^{10}$) is divided by (100*99) + 1 is

• A. 1
• B. 100
• C. 9900
• D. none of these

Answer 1

The correct option is C 9900

Option (d)

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

(10x9)+1

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

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

$\frac{9^1}{91}$${|}_R$=-10

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

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

Remainder will be only the first part of the numerator=10x9, in the case we have considered = 90

And in the question = 100x99= 9900