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What is the remainder when $5^{99}$ is divided by 13?

Competition practiceNumber System, HCF & LCM

A8
B5
C12
D1

Step-by-Step Solution

5^{2} = 25 \equiv - 1

, so

5^{4} \equiv 1 (mod 13) .99 = 4 \times 24 + 3

, so

5^{99} \equiv 5^{3} = 125 = 9 \times 13 + 8

: remainder 8.

Answer: A) 8

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