2000 real numbers and roots of polynomials
Source: Iran TST 2012-Third exam-1st day-P2
May 15, 2012
algebrapolynomialpigeonhole principlealgebra proposed
Problem Statement
Do there exist real numbers (not necessarily distinct) such that all of them are not zero and if we put any group containing of them as the roots of a monic polynomial of degree , the coefficients of the resulting polynomial (except the coefficient of ) be a permutation of the remaining numbers?Proposed by Morteza Saghafian