Given fβZ[x] and nβZ+, the
\emph{discriminator}Dfβ(n) is the smallest positive integer m such that
f(1),β¦,f(n) are distinct mod m. In a recent paper, Z.-W. Sun proved
that Dfβ(n)=dβlogdβnβ if f(x)=x(dxβ1) for dβ{2,3}. We extend this result to d=2r for any rβZ+
and find that Dfβ(n)=2βlog2βnβ in this case. We also
provide more general statements for d=pr, where p is a prime. In
addition, we present a potential method for generating prime numbers with
discriminators of polynomials which do not always take prime values. Finally,
we describe some general statements and possible topics for study about the
discriminator of an arbitrary polynomial with integer coefficients.Comment: 8 page