MathDB

A polynomial

P

with integer coefficients is square-free if it is not expressible in the form

P = Q^2R

, where

Q

and

R

are polynomials with integer coefficients and

Q

is not constant. For a positive integer

n

, let

P_n

be the set of polynomials of the form

1 + a_1x + a_2x^2 + \cdots + a_nx^n

with

a_1,a_2,\ldots, a_n \in \{0,1\}

. Prove that there exists an integer

N

such that for all integers

n \geq N

, more than

99\%

of the polynomials in

P_n

are square-free.
Navid Safaei, Iran

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