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Sequences and polynomials

Source: Iranian 3rd round 2016 first Algebra exam

August 13, 2016
algebrapolynomial

Problem Statement

Do there exists many infinitely points like (x1,y1),(x2,y2),...(x_1,y_1),(x_2,y_2),... such that for any sequences like {b1,b2,...b_1,b_2,...} of real numbers there exists a polynomial P(x,y)∈R[x,y]P(x,y)\in R[x,y] such that we have for all ii : P(xi,yi)=biP(x_{i},y_{i})=b_{i}
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