When 3^{333} is divided by 11, the remainder is
Question:
When 3^{333} is divided by 11, the remainder is
When 3^{333} is divided by 11, the remainder is
Options
Answer: 5
Explanation:
We need the remainder when 3^333 is divided by 11. Step 1: Use Fermat's Little Theorem For prime p = 11: a^(p−1) ≡ 1 (mod p), if a is not divisible by p. So: 3^10 ≡ 1 (mod 11) Step 2: Reduce the exponent modulo 10 333 ÷ 10 = 33 remainder 3 So: 3^333 ≡ 3^3 (mod 11) Step 3: Compute 3^3 modulo 11 3^3 = 27 27 mod 11 = 27 − 22 = 5 Answer: 5
Explanation:
We need the remainder when 3^333 is divided by 11. Step 1: Use Fermat's Little Theorem For prime p = 11: a^(p−1) ≡ 1 (mod p), if a is not divisible by p. So: 3^10 ≡ 1 (mod 11) Step 2: Reduce the exponent modulo 10 333 ÷ 10 = 33 remainder 3 So: 3^333 ≡ 3^3 (mod 11) Step 3: Compute 3^3 modulo 11 3^3 = 27 27 mod 11 = 27 − 22 = 5 Answer: 5
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