AP EAMCET · Maths · Basic of Mathematics
The remainder obtained when \(5^{99}\) is divided by 13 is
- A 6
- B 7
- C 8
- D 9
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
\(5^2 \equiv 25 \equiv -1 \pmod{13}\) \(5^{99} \equiv (5^2)^{49} \cdot 5^1 \pmod{13}\) \( \equiv (-1)^{49} \cdot 5 \pmod{13}\) \( \equiv -1 \cdot 5 \pmod{13}\) \( \equiv -5 \pmod{13}\) \( \equiv 8 \pmod{13}\)
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