1. The problem is to construct an addition table in modulo 4. 2. In modulo arithmetic, addition is performed and then the remainder when divided by the modulus is taken. 3. The formula for addition modulo $n$ is $$a + b \equiv (a + b) \bmod n$$ where $a$ and $b$ are integers and $n$ is the modulus. 4. Here, $n=4$, so we calculate $a + b \bmod 4$ for $a,b \in \{0,1,2,3\}$. 5. Construct the table by adding each pair and taking the remainder modulo 4: | + | 0 | 1 | 2 | 3 | |---|---|---|---|---| | 0 | 0 | 1 | 2 | 3 | | 1 | 1 | 2 | 3 | 0 | | 2 | 2 | 3 | 0 | 1 | | 3 | 3 | 0 | 1 | 2 | 6. Explanation: For example, $2 + 3 = 5$, and $5 \bmod 4 = 1$, so the entry at row 2, column 3 is 1. 7. This table shows all possible sums modulo 4, which is useful in modular arithmetic and number theory.