MODULAR ARITHMETIC 101

You already know modular maths, thanks to how we read clocks.

Modular arithmetic gets its name from the modulo operator (mod for short), which dictates how you’ll count through a series of numbers. On a clock, the mod is 12. We count up to 12 and then start over again. Which is why 3 pm is not 15 pm, but 3 is congruent (essentially, equal) with 15 (mod 12).

The modulo operator can be any positive number, and acts as the key for understanding how the values of numbers have changed. For example, in mod 2, the numbers 3 and 5 are the same.

In modular arithmetic, your mod value is how many numbers are in your mod.

But unlike the numbers on a clock, we start with 0 where 12 would be. So mod 2 includes the numbers 0 and 1 but not 2. There are two numbers in the mod, but the actual number of the mod (say, mod 2) is not in the mod, because we start at zero. 3 and 5 are congruent in mod 2 because they’re both 1. Likewise, 0, 2, and 4 are all 0.