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    • Modular Arithmetic

    To work out what 17 mod 12 is, divide 17 by 12 and keep the remaninder:

    17 divided by 12 is 1 remainder 5 so 17 mod 12 is 5
    Check that this rule works for our other examples.

    Now there is nothing special about working mod 12 -- that just came from our example of the clock. Here is some practice:

    • 32 mod 11
    • 11 mod 32
    • 2 mod 5
    • 5 mod 2
    • 7 mod 1
    • 1 mod 7
    Write down your answers and then check them.

    Can you formulate the rule in general? What does

    a=b mod n
    mean? Here is my answer.