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How do I solve for negative modular arithmetic?

Here is an example: -45 mod 13 = 7, but how?

  • Math - ,

    a mod b = (a + nb) mod b

    so, -45 mod 13 = mod (-45 + 52) mod 13 = 7 mod 13 = 7

    Just add a big enough multiple of the modulus so you have a positive number.

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