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CIIM 2018 Problem 2

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March 9, 2019
CIIM2018undergraduatealgebrapolynomial

Problem Statement

Let p(x)p(x) and q(x)q(x) non constant real polynomials of degree at most nn (n>1n > 1). Show that there exists a non zero polynomial F(x,y)F(x,y) in two variables with real coefficients of degree at most 2n−2,2n-2, such that F(p(t),q(t))=0F(p(t),q(t)) = 0 for every t∈Rt\in \mathbb{R}.
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