Y by cheaterzeta
Let
be positive integers and
be a set of lattice points. Prove that if
then there exists a circle which passes through at least four distinct points of 

![$S\subseteq [1,m]\times [1,n]$](http://latex.artofproblemsolving.com/d/0/0/d006a3ac6d141c445a1cedacb9f8955cb35e338f.png)
![\[|S|\geq m+n+\bigg\lfloor\frac{m+n}{4}-\frac{1}{2}\bigg\rfloor\]](http://latex.artofproblemsolving.com/3/a/4/3a4c798654d9a2d264adb6ed0190adf2a53fcf5c.png)

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