2020 USAMO Problems/Problem 5: Difference between revisions
Created page with "== Problem == A finite set <math>S</math> of points in the coordinate plane is called <i>overdetermined</i> if <math>|S| \ge 2</math> and there exists a nonzero polynomial <ma..." |
m →Solution: newbox |
||
| Line 7: | Line 7: | ||
{{Solution}} | {{Solution}} | ||
{{USAMO | {{USAMO newbox|year=2020|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 09:15, 31 July 2023
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
| 2020 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
