MathDB

Find all polynomials

P(x)

of odd degree

d

and with integer coefficients satisfying the following property: for each positive integer

n

, there exists

n

positive integers

x_1, x_2, \ldots, x_n

such that

\frac12 < \frac{P(x_i)}{P(x_j)} < 2

and

\frac{P(x_i)}{P(x_j)}

is the

d

-th power of a rational number for every pair of indices

i

and

j

with

1 \leq i, j \leq n

Problem Statement