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How do I solve for negative modular arithmetic?

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

  • Math -

    -52 mod 13 = 0
    -45-(-52)=7

  • Math -

    You can add multiples of 13 until you get a positive number, example:
    -45+4(13)=-45+52=7
    or even
    -45+10(13)=-45+130=85≡7 mod 13

  • Math -

    Thanks for your help!

    Also, I am kind of confused about finding the value of x.

    Example: 9x ≡ 1 mod 10

    How do I solve this?

  • Math -

    how long will it take for a 10,000 investment to grow to 15,000if it is compounded continuously at 5 %

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