Eduprobe
Question:
The remainder left out when 82n−(62)²ⁿ⁺¹ is divided by 9 is
7
2
8
0
Solution:
82ⁿ−(62)²ⁿ⁺¹ →(63+1)ⁿ−(63−1)²ⁿ⁺¹ →(63+1)ⁿ+(1−63)²ⁿ⁺¹ →(1+ⁿC₁(63))+(1−²ⁿ⁺¹C₁(63)..)→2+63(ⁿC₁+ⁿC₂(63)..)So, the remainder will be 2Hence, option 'B' is correct.