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SMO 2021 Open Round 1 Question 6

SMO · SMO 2021 Open Round 1

Question 6

Consider all the polynomials $P(x,y)$ in two variables such that $P(0,0)=2020$ and for all $x$ and $y$, $P(x,y)=P(x+y,y-x)$. Find the largest possible value of $P(1,1)$.