Modular Arithmetic

It will be important to understand a simple transformation that's possible with modular arithmetic. These 2 formulas are effectively equivalent:

n ≡ r (mod q)
n = qk + r

Where n is the number we're working with, r is the remainder, q is the divisor, and k is the number of times q goes into n. This allows us to convert an equation in the world of modular arithmetic into a more familiar equation in the normal world.

For example,

9 ≡ 1 (mod 2)

Can be converted to:

9 = 2k + 1

This will be important later.