MathDB

Prove that, for every pair

n

r

of positive integers, there can be found a polynomial

f(x)

of degree

n

with integer coefficients, so that every polynomial

g(x)

of degree at most

n

, for which the coefficients of the polynomial f(x)\minus{}g(x) are integers with absolute value not greater than

r

, is irreducible over the field of rational numbers.

Problem Statement