What is the remainder when 2^{120} is divided by 7?
- A. 1 ✓
- B. 3
- C. 5
- D. 6
Correct Answer: A. 1
Explanation
We can rewrite 2^{120} in powers of 2^3 because 2^3 = 8 \equiv 1 \pmod 7. Thus, 2^{120} = (2^3)^{40} = 8^{40}. Since 8 \equiv 1 \pmod 7, we have 8^{40} \equiv 1^{40} \equiv 1 \pmod 7. The remainder is 1.
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