Representation of unars by sets of residues

We find faithful representations of a finite unar (an algebra with one unary operation on a finite set) in some standard constructions. We prove that every finite unar can be faithfully represented by the residues modulo $n$ with the operation $f(x)= x\cdot a \,\mod n$ for suitable $n$ and $a$. Besides, for every integer $d\ge 2$, there exists a faithful representation of every finite unar by residues modulo $n$ with the operation $f(x)= x^d \,\mod n$ for suitable $n$. Further, for any $d\ge 3$, every finite unar can be faithfully presented by invertible residues modulo $n$ with the operation $f(x)= x^d \,\mod n$ for suitable $n$. (The later assertion is not true for $d=2$).