The minimal residue of is the value b or , whichever is smaller in absolute value, where . If (so that ), then the minimal residue is taken as . The table below illustrates the common (positive) and minimal residues for 0, 1, 2, and 3 (mod 4).

n	common residue	minimal residue
0	0	0
1	1	1
2	2	-2
3	3	-1

The minimal residue is implemented in Mathematica as Mod[a, m, -m/2].

Common Residue, Congruence, Modulus, Residue

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