10 numbers forming 500 "good" quadratic trinomials
Source: St. Petersburg MO 2001 Grade 9 Problem 2
March 1, 2023
quadraticsalgebraquadratic trinomialrootsSt. Petersburg MO
Problem Statement
Define a quadratic trinomial to be "good", if it has two distinct real roots and all of its coefficients are distinct. Do there exist 10 positive integers such that there exist 500 good quadratic trinomials coefficients of which are among these numbers?[I]Proposed by F. Petrov