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Modular Arithmetic and Graphs
Modular Arithmetic and Graphs
Modular arithmetic studies remainders. Graph theory studies networks of vertices and edges.
Congruence Modulo $n$
We write $$a \equiv b \pmod{n}$$ if $a$ and $b$ have the same remainder when divided by $n$.
Example 1
Compute $17 \bmod 5$.
The remainder is $2$.
Example 2
Is $23 \equiv 5 \pmod 9$?
Yes, both leave remainder $5$.
Graph Vocabulary
A graph has vertices (points) and edges (connections). The degree of a vertex is the number of edges touching it.
Practice Problems
1. Compute $14 \bmod 4$.
2. Compute $31 \bmod 6$.
3. What does $a \equiv b \pmod n$ mean?
4. What is a vertex?
5. What is the degree of a vertex?
Show Answer Key
1. $2$
2. $1$
3. They have the same remainder when divided by $n$
4. A node or point in a graph
5. The number of incident edges