Posted by **Francesca ** on Monday, October 10, 2011 at 12:52pm.

How do I solve for negative modular arithmetic?

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

- Math -
**Mgraph**, Monday, October 10, 2011 at 12:56pm
-52 mod 13 = 0

-45-(-52)=7

- Math -
**MathMate**, Monday, October 10, 2011 at 12:56pm
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 -
**Francesca **, Tuesday, October 11, 2011 at 11:12am
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?

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**Anonymous**, Thursday, June 28, 2012 at 10:41pm
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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