Modulus of negative numbers

AARRRGH

Hello

I really hope someone can help me with this.

I am reading lecture notes and it says the following -

-12 mod 11 = 10
-1 mod 11 = 10

When I do -12 mod 11 and -1 mod 11 on my calculator I get -1 for both.

Is there a trick or something extra I am missing here?

Note I am dealing with finite fields.

Any help greatly appreciated.

Thanks

AARRRGH

I think the answer has something to do with 22 - 10 = 11, where 22 is a multiple of 11 which is greater than 12.

Why doesn't the % (in C) and a calculator give the correct answer?

LeixlipRed

When it says = 10 it means 10(mod 11). -12 = (-2)(11) + 10 and -1 = (-1)(11) + 10. Not sure you understand modular arithmetic fully to be honest. Or maybe that's not the question you're asking?

bobzi

Hi dublindude,

when working with modular arithmetic in a finite field the remainder should always be non-negative so:
-12 = -2*11+10 => -12 mod 11 = 10
-1 = -1*11+10 => -1 mod 11 = 10

AARRRGH

Thank you for the replies.

bobzi wrote:

when working with modular arithmetic in a finite field the remainder should always be non-negative so:
-12 = -2*11+10 => -12 mod 11 = 10
-1 = -1*11+10 => -1 mod 11 = 10

Is this the same as saying if the answer is a minus, just add the modulus to it?

For example, -12 mod 11 = -1. -1 + 11 = 10.

Or is that just coincidence?

bobzi

yeah that'll work

LeixlipRed

dublindude wrote: »

Thank you for the replies.



Is this the same as saying if the answer is a minus, just add the modulus to it?

For example, -12 mod 11 = -1. -1 + 11 = 10.

Or is that just coincidence?

That's the whole idea basically.

a is congruent to b (mod n) where a= kn + b. ie some multiple of your modulus plus the remainder. So if a number is outside your "window", i.e. from 0 to n-1 then to bring it inside you can add or subtract multiples of n.

AARRRGH

Thanks guys!