Question:

The remainder when $4^{28^{2024}}$ is divided by 21 is __________.

Step-by-Step Solution

Key Concept: $428^{2024}\equiv8^{2024}\pmod{21}$. $8^2=64\equiv1\pmod{21}$. $8^{2024}=(8^2)^{1012}\equiv1$.

Remainder $=1$.

Correct Answer: 1