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A two var poly is linear comb of (x+ay)^k

Source: 2017 South Korea USCM P2

August 15, 2020
polynomiallinear algebraalgebracollege contests

Problem Statement

Show that any real coefficient polynomial f(x,y)f(x,y) is a linear combination of polynomials of the form (x+ay)k(x+ay)^k. (aa is a real number and kk is a non-negative integer.)