For odd primes p=3 (mod 4), the number of residues & non-residues is equal, and every element of GF(p) can be represented as 0, r or -r, where r is a quadratic residue. Thus, if p=3, the representatives are 0,1,-1. If p=7, the representatives are 0,1,2,4,-1,-2,-4. If p=11, the representatives are 0,1,3,4,5,9,-1,-3,-4,-5,-9. So, are there any advantages to using *only* residues (or alternatively, non-residues) as *representatives* mod p? In particular, if we consider expressing integers *base p* for a base p=3(mod 4), and we utilize only residues and negative residues for our "digits", do any interesting patterns arise? E.g., for base p=3, the digits in this representation are simply Knuth's "trits". Is there already a name for this type of number base representation (We have to be a tad careful when doing the base conversion; I'm not worried about the complexity of the conversion itself for the moment.) Due to the strong analogy with positive & negative (real) numbers, there may be interesting analogues in matrix problems mod p using this representation.