Question 26
Consider $M=\{1,2,3,\ldots,2019,2020\}$. Find the smallest positive integer $k$ with the following property: for every $k$-element subset $A$ of $M$, there exist three pairwise distinct numbers $a,b,c\in M$ such that $a+b$, $b+c$, and $c+a$ all belong to $A$.