The remainder when \( \Large 9^{19}+6 \) is divided by 8 is


A) 2

B) 3

C) 5

D) 7

Correct Answer:
D) 7

Description for Correct answer:
Required remainder = \( \Large 9^{19} \) + 6

= \( \Large (1)^{19}+6 \)=9

[ 8=9-1,so replaced by 1]

We have = \( \Large \frac{(9)^{19}+6}{8} \)

=> \( \Large \frac{(8+1)^{19}+6}{8} \) => \( \Large \frac{1^{19}+6}{8} \)

=> \( \Large \frac{1+6}{8}=\frac{7}{8} \)

Remainder = 7

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