MathDB

Let

I

be an ideal of the ring

\mathbb{Z}\left[x\right]

of all polynomials with integer coefficients such that
a) the elements of

I

do not have a common divisor of degree greater than

0

, and
b)

I

contains of a polynomial with constant term

1

.
Prove that

I

contains the polynomial

1 + x + x^2 + ... + x^{r-1}

for some natural number

r

.
Gy. Szekeres

4