Journal of Integer Sequences, Vol. 22 (2019), Article 19.1.1 |

Department of Mathematics

School of Science

Siena College

Loudonville, NY 12211

USA

**Abstract:**

We study the uniform distribution of the polynomial sequence
modulo integers, where
*P*(*x*) is a polynomial with real coefficients. In the nonlinear case, we
show that
is uniformly distributed in
if and
only if *P*(*x*) has at least one irrational coefficient other than the
constant term. In the case of even degree, we prove a stronger result:
intersects every congruence class modulo every integer if
and only if *P*(*x*) has at least one irrational coefficient other than
the constant term.

Received September 11 2018; revised version received December 16 2018.
Published in *Journal of Integer Sequences*,
December 17 2018.

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