Negative numbers in modular division

[colerelm]

I know how modular division works with positive integers but how would I solve something like -19 mod 48? I can't even begin to think of how this makes any sense or how to approach the problem. Any help would be appreciated.

Thanks

 

[daon2]

I know how modular division works with positive integers but how would I solve something like -19 mod 48? I can't even begin to think of how this makes any sense or how to approach the problem. Any help would be appreciated.

Thanks

a = a+kc (mod c) for all integers k. That is, adding multiples of c to a preserves the value modulo c.

So -18 (mod 48) = -18 + 48 (mod 48) = 30 (mod 48)

 

[HallsofIvy]

As daon2 showed, any integer, modulo n, can be represented by a number larger than or equal to 0 and less than n.