MathDB

We call a polynomial

P(x)=a_dx^d+...+a_0

of degree

d

nice if

\frac{2021(|a_d|+...+|a_0|)}{2022}<max_{0 \le i \le d}|a_i|

Initially Shayan has a sequence of

d

distinct real numbers;

r_1,...,r_d \neq \pm 1

. At each step he choose a positive integer

N>1

and raises the

d

numbers he has to the exponent of

N

, then delete the previous

d

numbers and constructs a monic polynomial of degree

d

with these number as roots, then examine whether it is nice or not. Prove that after some steps, all the polynomials that shayan produces would be nice polynomials
Proposed by Navid Safaei

Problem Statement