Discussion

What is the remainder when \(5^5\) is divided by 3?

Answer: C

First, find the remainder of the base. \(5 \div 3\) leaves a remainder of 2. So the problem is equivalent to finding the remainder of \(2^5 \div 3\). \(2^5=32\). Now, find the remainder of \(32 \div 3\). The sum of digits is 5, and \(5 \div 3\) leaves a remainder of 2. So the remainder is 2. Alternatively, \(2 \equiv -1 \pmod{3}\), so \(2^5 \equiv (-1)^5 = -1 \equiv 2 \pmod{3}\).