Abstract
Let
p
n
$p_n$
p Subscript n
denote the
n
th prime. We prove that, for every nonzero polynomial
f
(
x
)
∈
Z
[
x
]
$f(x)\in \mathbb {Z}[x]$
f left parenthesis x right parenthesis element of double struck upper Z left bracket x right bracket
, there exist infinitely many positive integers
n
such that
p
n
∤
f
(
n
)
$p_n\nmid f(n)$
p Subscript n Baseline does not divide f left parenthesis n right parenthesis
.