Divisibility of Sums and Products
Big Idea: When we know that certain numbers are divisible by some integer, we can determine whether their sums, differences, and products are also divisible by that integer — without ever computing the actual values!
📌 Key Definitions
Divisibility: We say an integer $a$ is divisible by an integer $d \neq 0$ (written $d \mid a$) if there exists an integer $k$ such that $a = d \cdot k$.
For example, $12$ is divisible by $3$ because $12 = 3 \cdot 4$.