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Modular Multiplication


The beauty of modular arithmetic is that you never need to manipulate any huge numbers. How big 'huge' is depends on the modular base. For instance, when you take products of many numbers and you want to find their remainder modulo n, you never need to worry about numbers bigger than the square of n.

First a couple of examples:

Pick any two numbers x and y, and look at their remainders (mod 7):

a = x (mod 7) b = y (mod 7) .
Compare the remainder modulo 7 of the products xy and ab:

xy (mod 7) with ab (mod 7)

Practice
Modular product

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