p(x)=a(x) +b(x), squares of polynomials
Source: Tournament of Towns, Senior Ο-Level Paper, Spring 2020 , p4
June 4, 2020
algebrapolynomial
Problem Statement
We say that a nonconstant polynomial with real coefficients is split into two squares if it is represented as where and are squares of polynomials with real coefficients. Is there such a polynomial that it may be split into two squares:
a) in exactly one way;
b) in exactly two ways?Note: two splittings that differ only in the order of summands are considered to be the same.Sergey Markelov