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Introduction to Modular Arithmetic and Equivalence Classes

What’s the remainder of 6 when it’s divided by 5? One!

We can write: $6 = 5 \cdot 1 + 1$

What’s the remainder of 10 when divided by 5? Zero!

We can write: $10 = 5 \cdot 2 + 0$

You’ve probably encountered modular arithmetic, which is a formal way of asking “what’s the remainder of number $a$ when it’s divided by $n$?”