2020 USAMO Problems/Problem 5
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Problem
A finite set 
of points in the coordinate plane is called overdetermined if 
and there exists a nonzero polynomial 
, with real coefficients and of degree at most 
, satisfying 
for every point 
.
For each integer 
, find the largest integer 
(in terms of 
) such that there exists a set of distinct points that is not overdetermined, but has overdetermined subsets.
Solution
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