Numbers on blackboard
Source: Tournament of Towns 2016 oral round p6
March 21, 2016
Polynomialsnumber theoryalgebra
Problem Statement
different numbers are written on blackboard and one of these numbers is equal to .One may take any polynomial such that each of its coefficients is equal to one of written numbers ( there may be some equal coefficients ) and write all its roots on blackboard.After some of these operations all integers between and were written on blackboard(and some other numbers maybe). Find the smallest possible value of .