MathDB
p(cos t, sin t) = 0, p(x,y) = (x^2 + y^2 - 1) q(x,y), polynomials

Source: 1985 Polish MO Finals p5

January 21, 2020
polynomialalgebra

Problem Statement

p(x,y)p(x,y) is a polynomial such that p(cost,sint)=0p(cos t, sin t) = 0 for all real tt. Show that there is a polynomial q(x,y)q(x,y) such that p(x,y)=(x2+y2āˆ’1)q(x,y)p(x,y) = (x^2 + y^2 - 1) q(x,y).
Back to ProblemsView on AoPS