The remainder when \(6^{1029}\) is divided by 7 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6
Since 6 is one less than 7:
\(6 \equiv -1 \pmod 7\)
Powers keep the congruence, and 1029 is odd:
\(6^{1029} \equiv (-1)^{1029} = -1 \pmod 7\)
\(-1 \equiv 6 \pmod 7\)
So the remainder is 6.