MathDB

Whether exist set

A

that contain 2016 real numbers (some of them may be equal) not all of which equal 0 such that next statement holds. For arbitrary 1008-element subset of

A

there is a monic polynomial of degree 1008 such that elements of this subset are roots of the polynomial and other 1008 elements of

A

are coefficients of this polynomial's degrees from 0 to 1007.

Problem Statement