Find the unit digit of \(3^{4n+1}\), where n is a positive integer.
Answer: B
The unit digit of powers of 3 follows a cycle of length 4: (3, 9, 7, 1). To find the unit digit, we need the remainder of the power when divided by 4. The power is \(4n+1\). When \(4n+1\) is divided by 4, the term \(4n\) is perfectly divisible, leaving a remainder of 1. A remainder of 1 corresponds to the first digit in the cycle, which is 3.