If the number 11⁶ is divided by 7, the remainder is:
2019
If the number 11⁶ is divided by 7, the remainder is:
- A.
1
- B.
3
- C.
4
- D.
2
Attempted by 82 students.
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Correct answer: A
Solution: Use modular arithmetic to find the remainder.
Reduce the base modulo 7: 11 ≡ 4 (mod 7).
Square to simplify the exponent: 11^2 ≡ 4^2 = 16 ≡ 2 (mod 7).
Use that 11^6 = (11^2)^3, so 11^6 ≡ 2^3 = 8 ≡ 1 (mod 7).
Therefore the remainder when 11^6 is divided by 7 is 1.
Answer: 1