> why is f(0) in an ll test = 4

Well, it needn't be.  There are a number of other possibilities, but 4 is the
smallest...

> also when i went to sshool (i'm 34) 7 mod 8 == 7
> i have seen 7 mod 8 == -1
> is  -1 == 7 mod 8
> which is more correct

They are both correct.  If you have a congruence relation (mod n), then 
you can add n to either side (it's like adding or subtracting zero).

-Lucas
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