MathDB

Let

p(x) = a_{21} x^{21} + a_{20} x^{20} + \dots + a_1 x + 1

be a polynomial with integer coefficients and real roots such that the absolute value of all of its roots are less than

1/3

, and all the coefficients of

p(x)

are lying in the interval

[-2019a,2019a]

for some positive integer

a

. Prove that if this polynomial is reducible in

\mathbb{Z}[x]

, then the coefficients of one of its factors are less than

a

.
Submitted by Navid Safaei, Tehran, Iran

Problem Statement