This is a sub-page of our page on Interactive Learning Objects.

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Experiment here with different arithmetical operations.

Whenever you feel like it, you are invited to try out a “field characteristc” different from zero, and investigate what happens. Can you figure out what is going on here? In mathematese ( = the language of mathematics) we call it modular arithmetic and it obeys the rule:

x+n \times a \equiv x \pmod a , \forall \, x, n, a \in \mathrm Z.

What this formula means (in plain English) is that the integers x and x + n \times a have the same remainder when you divide them by the integer a.

Modular Arithmetic Visually Explained
(Zach Star on YouTube):

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