MathDB

Let

N{}

be the number of positive integers with

10

digits

\overline{d_9d_8\cdots d_0}

in base

10

(where

0\le d_i\le9

for all

i

and

d_9>0

) such that the polynomial

d_9x^9+d_8x^8+\cdots+d_1x+d_0

is irreducible in

\Bbb Q

. Prove that

N

is even.
(A polynomial is irreducible in

\Bbb Q

if it cannot be factored into two non-constant polynomials with rational coefficients.)

Problem Statement